what is factoring: problems involving factors of polynomials

Answers

Answer 1

Answer: Factoring is essentially the reverse of the distributive property. You are basically trying to simplify the polynomial by taking out common factors. You also may try reducing the power (or the highest exponent) of the polynomial with factoring. I would say that factoring is the breaking down of a bigger polynomial into a product of two expressions that are usually multiplied by each other. One specific use of factoring we see a lot is the quadratic formula.

1. Quadratic Factoring --> [tex]x^2+2x-15[/tex] --> we have an [tex]x^2[/tex] but we want there to only be "[tex]x[/tex]"s. Here we need to constant numbers (integers), that multiply together to get [tex]-15[/tex], and add up to [tex]+2[/tex]. (5 and -3)

    - [tex]x^2+2x-15[/tex] ==> [tex]x^2+5x-3x-15[/tex] ==> [tex]x(x+5)-3(x+5)[/tex] ==> [tex](x-3)(x+5)[/tex]

Above: We can see that we factor out [tex]x[/tex] from [tex]x^2+5x[/tex] (This shows that we are aiming to break it down to make it easier to evaluate).

Remember: Factoring does not always mean that the polynomial is in a simpler form. There are many situations where factoring is totally unnecessary and complicates the polynomial even more.

--------------------------------------------------------------------------------------------------------------On a separate note: Distributive Property, if you are unsure or not fully sure on what that means, is when you multiply two expressions together to create one expression. Multiple expressions are combining into one.

Answer 2
For example, factor 6x²+10x as 2x(3x+5).

Factoring out the greatest common factor (GCF)
Find the GCF of all the terms in the polynomial.
Express each term as a product of the GCF and another factor.
Use the distributive property to factor out the GCF.

Related Questions

13-n + 2n > 8 + 1 Solve the given inequality and graph and solution

Answers

because we are finding for the variable and not the coefficient we divide it by the number attached to the variable which is the coefficient to get the result of the variable

A pair of shoes sell for $75 from the manufacturing company. If the store sells the shoes for $150 dollars what is the mark-up (percent increase) of the price of the shoe from the manufacturing company to the store?
Help

Answers

The mark-up (percent increase) of the price of the shoe from the manufacturing company to the store is 100%.

Given the following data:

Cost price = $75 Selling price = $150

To determine the mark-up (percent increase) of the price of the shoe from the manufacturing company to the store:

First of all, we would determine the increase in price of this shoe:

[tex]Increase = selling\;price -cost\;price\\\\Increase = 150-75[/tex]

Increase = $75

For mark-up (percent increase):

[tex]Mark\;up = \frac{Increase}{Cost\;price} \times 100\\\\Mark\;up = \frac{75}{75} \times 100[/tex]

Mark-up = 100%

Read more on mark-up here: https://brainly.com/question/25790940


Please help!! I need this ASAP

Answers

Answer:

a= 2.5 times 42

Step-by-step explanation:

i had this class last year

School yearbooks were printed and the table shows the number of people who bought them the first, second, third, and fourth weeks after their release .which graph could represent the data shown in the table? Table and options below!


PLS HURRY!30 POINTS ANS BRAINLEST!

Answers

Answer: The correct graph that would depict the table correctly would be the first one listed. There is a sudden increase in the last day which would cause the graph to curve. Hope this helps you out! If you need anything else I'm here to help.

The function is an increasing function. The graph that represents the table will be A.

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The table is given below.

Week     Number of sales

  1                    84

 2                   102

 3                   158

 4                   271

The slope at different will be given as,

m₁ = (102 - 84) / (2 - 1)

m₁ = 18

m₂ = (158 - 102) / (3 - 2)

m₂ = 56

m₃ = (271 - 158) / (4 - 1)

m₃ = 113

The capability is a rising capability. The diagram that addresses the table will be A.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

there are 47 students in the science club. all but 5 of them went on a field trip to the planetarium. what is the total cost if each student who went on the field trip paid $7?

Answers

Answer:

294

Step-by-step explanation:

40x7=280

2x7=14

280+14=294

Answer:

$294

Step-by-step explanation:

There is a total of 47 students in the science club.

5 did not go on the trip.

Number of students who went on the trip: 47 - 5 = 42

42 students wen on the trip.

Cost per person: $7

Total cost for 42 students: 42 × $7 = $294

If 4 bushels of oats weigh 112 kg, how much do 8. 5 bushels of oats weigh?.

Answers

Answer:

238 kg

Step-by-step explanation:

If 4 bushels weight 112, then divide 112 by 4 and you get that each bushel weighs 28 kg. Now multiply that by 8.5.

Mr. Williams drew the following image on the board and asked his students to write a sequence of steps explaining how to construct a line which passes through point C and is perpendicular to line AB. The work of two students, Elias and Greyson, is shown.

Answers

.shown is, Greyson and Elias, students two.

Answer:

both Elias and Greyson

Step-by-step explanation:

If I have a ramp of 8 feet in length and 4 feet in height what is the diagonal length and degree

Answers

Answer:

almost 9

Step-by-step explanation:

These are samples of student work. Both students got the same answer, but did the work differently. Which student did the work correctly?

Answers

Answer:

Student B did the problem corectly

Step-by-step explanation:

Student a did 3*4 while student B did 3*3*3*3 which would equal 27

Eva earns $5.50 per hour and time-and-a-half for overtime for all hours over 40 hours. How much did she earn the week she worked 47 hours?

Answers

Answer:

$277.75

5.50×40=220

5.50÷2=2.75

5.50+2.75=8.25×7=57.75

57.75+220=277.75

ursula drew a polygon in which all the angels were obtuse. what kind of polygon could she have drawn

Answers

Answer:  Hexagon

Explanation:

There are n = 6 sides to a hexagon. If we had a regular hexagon, then each exterior angle is E = 360/n = 360/6 = 60 degrees, which means the adjacent interior angle is 180-E = 180-60 = 120.

In short, each interior angle of a regular hexagon is 120 degrees, making each angle obtuse. Other polygons are possible for the answer.

HURRY QUICK!!

Evaluate the following expression when x = -4 and y = 4.

Answers

Answer: Should be A

Step-by-step explanation:

Not 100% sure but I'm pretty sure it's A

Answer:

A

Step-by-step explanation:

You need to insert the values into the equations

1) [tex]\frac{x^{6} -x}{4y}[/tex]

[tex]\frac{(-4)^{6} -(-4)}{4(4)}[/tex]

Then open the brackets

[tex]\frac{4096 -(-4)}{16}[/tex]

Open the brackets again not forgetting that 2 - equal a positive

[tex]\frac{4100}{16}[/tex]

Simplify

[tex]\frac{1025}{4}[/tex]

Angle A is in standard position and terminates in quadrant IV. If sec(A)=4 3 , complete the steps to find cot(A). Use the identity to find the value of (A).

Answers

If sec(A) = 4/3, then the value cot(A) is [tex]cot(A)=\frac{3\sqrt{7}}{7}[/tex]

The given trigonometric identity is:

[tex]sec(A)=\frac{4}{3}[/tex].........................(*)

Note that:

[tex]sec(A)=\frac{Hypotenuse}{Adjacent}[/tex].........................(**)

Comparing (*)  and (**)

Hypotenuse = 4

Adjacent = 3

Find the opposite using the Pythagoras theorem

Hypotenuse²  =  Opposite²  +  Adjacent²

4²   =  Opposite²  +  3²

Opposite² = 4²  -  3²

Opposite²  =  16 - 9

Opposite² = 7

Opposite = √7

cot(A) = Adjacent/Opposite

cot(A) = 3/√7

Rationalize the expression

[tex]cot(A)=\frac{3\sqrt{7}}{7}[/tex]

Learn more here: https://brainly.com/question/25913087

Answer

1A=B 1B=tan 2=B 3=A

Step-by-step explanation:

Chance and Destiny went shopping at New Fashion Shop,
Everything in the store was at a 30% discount. Chanice
found a dress that was originally $65.00. What was the sale price?

Answers

$65 of 30% discount
$65-$19.50=$45.50
The sale price would be $45.50

The quadratic function g(x)=ax^2+bx+c has the complex roots (-5+9i) and (-5-9i).
What is the value of a?
What is the value of b?
What is the value of c?

Answers

Answer:

I don't know sorry

PLEASE NO LINKS AND NO NEGATIVITY

Answers

-4w+32
multiply using the distributive property

Suppose in order for a bill to pass in Congress, 50% of voters must be in favor of it. In a random sample of 150 voters, 62 said that they were in favor of a new bill. State the p-value assuming the alternative hypothesis is Ha ≠.50 (Round to the nearest hundredth.)

Answers

Using the z-distribution, it is found that the p-value is of 0.03.

At the null hypothesis, it is tested if the proportion is of 0.5, that is:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, it is tested if the proportion is different of 0.5, that is:

[tex]H_a: p \neq 0.5[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.

For this problem, the parameters are: [tex]p = 0.5, n = 150, \overline{p} = \frac{62}{150} = 0.4133[/tex]

Hence, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.4133 - 0.5}{\sqrt{\frac{0.5(0.5)}{150}}}[/tex]

[tex]z = -2.12[/tex]

The p-value is found using a z-distribution calculator, with z = -2.12 and a two-tailed test, as we are testing if the mean is different of a value, hence it is of 0.03.

To learn more about the use of the z-distribution for hypothesis tests, you can take a look at https://brainly.com/question/16313918

6) There are 350 calories in
cups of spaghetti. How
many calories are in two cups?
Working With Food

Answers

700 calories!
350*2= 700
700/2= 350
700/350= 2

h(x) = 72 - 1
Over which interval does h have a negative average rate of change?
Choose 1 answer:
-3<<5
1<2<4
-3<<1
-1<<5
3 of
4.00
Check

Answers

Answer:

you're right, keep it up! you're very smart

(Statistics)Which of the following is NOT a characteristic of a least squares regression line?

Answers

Based on the information given, the option that's correct is E. All the above are characteristics.

It should be noted that when the least square regression line goes through all the points, the sum of squared residuals is 0.

Also, the least-squares regression line makes the sum of the squares of the residuals as small as possible and the slope is usually between -1 and 1. The smaller the residual sum of squares, the better the model fits the data.

Learn more about the least square regression on:

https://brainly.com/question/16975425

What is the function graphed below?
3
Oy=x-1
Oy=1 X-1
Oy=1x+11
Oy=x+1

Answers

It would be x + 1 under the absolute value

The function that is graphed below is y = |x + 1|.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph of the equation y = |x + 1| is a V-shaped curve that opens upwards and has a vertex at the point (-1, 0).

The absolute value function, represented by the vertical bars surrounding the expression (x + 1), means that the function will always output a positive value, regardless of the input.

When x is greater than or equal to -1, the expression inside the absolute value bars is non-negative, so the equation simplifies to y = x + 1.

This is a linear function with a slope of 1 and a y-intercept of 1, which means that the graph of y = |x + 1| for x ≥ -1 is a straight line that passes through the point (-1,0) and slopes upward to the right.

When x is less than -1, the expression inside the absolute value bars becomes negative, so the equation simplifies to y = -(x + 1) = -x - 1.

This is also a linear function, but with a slope of -1 and a y-intercept of -1, which means that the graph of y = |x + 1| for x < -1 is a straight line that passes through the point (-1,0) and slopes downward to the right.

The two linear segments meet at the vertex (-1,0), which is the minimum point of the graph.

The graph of y = |x + 1| is a continuous, piecewise linear function with a minimum value of zero at x = -1.

Thus,

The function that is graphed below is y = |x + 1|.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ7

stions 5-7 the Grade 6 pupils graduated? In a school of 680 Grade 6 pupils, 646 graduated. What percent of the Grade 6 pupils graduated ? ​

Answers

Answer:

95% of Grade 6 pupils graduated

Answer:

95% of Grade 6 Pupils Graduated

Step-by-step explanation:

Express the Statement Mathematically:

646/680

Add Percentage

646/680 * 100%

By Division

0.95 * 100%

Then, Multiply

95%

36in rounded to the nearest tenth for circumference

Answers

Answer: Remember that the tens place is two moves to the left of the decimal point (if it exists). To round to the nearest ten (nearest 10), we use the whole numbers place to determine whether the tens place rounds up or stays the same.

Solution steps:

Step 1: Locate and underline the tens place () and look to digit to the right (6):

36

Step 2: In this case, the digit to the right 6 is 5 or above. So, we add 1 to the tens place (). The digit(s) after the (6) are dropped. Thus, we get 40 as answer.

In short: 36 rounded to the nearest tens is 40.

Step-by-step explanation:

work out the value of (3^(12) +3^(5) ) + (3^(2) x 3)

Answers

Answer:

the value of (3^(12) +3^(5) ) + (3^(2) x 3)=531711

A sign along the highway says 6% grade for the next 7 mi. How many feet of vertical change there are along those 7 miles. (5280 feet

Answers

Answer:

Step-by-step explanation:

The length of the road is 7 * 5280 = 36960 feet

The grade is 6% which means that for every 100 feet horizontally, the road rises 6 feet.

6/100 * 36960 = 221760/100 = 2217.6 is the rise.

There were approximately 16 million visitors to Disneyland in 2012. If the theme park is open every day of the year, about how many people visit per day?

Answers

approximately 43836 (rounded) people visit per day

50+10+23×61×80 please help mee!!​

Answers

Answer:

112300

Step-by-step explanation:

50+10+23*61*80

=60+23*61*80

=60+112240

=112300

The answer 112300, hope this helped :)

Answer:

I think the answer is 112,300.

Please help with this math problem!! IT'S DUE TONIGHT AT 11:59PM!! NO LINKS PLEASE!! :)

Answers

Answer:

[tex]c = \: \: 0 \: \: \: 1 \: \: 2 \: \: 3 \: \: 5 \: \: 7[/tex]

Step-by-step explanation:

check this pls

but im not sure;-)

pa heart and 5 star

if check po

Answer:

[tex]C= -2p+5, \text{where slope is} ~-2.[/tex]

Step by step explanation:

a store pays $60 for the shoes and sells them for $90. What is the percent markup

Answers

The markup is 20%!!!!

So far, Charlie has pures 456.6 Glories. He wants to burn a total of 500 calorierHow many more calories must Charlie burn?
| 0
2

Answers

Well if he’s burned 456.6 calories already and he needs to get to 500 then you would have to simply subtract 456.6 from 500
The equation: 500 - 456.6 = 43.4
Hope this helps!
Other Questions
simplify this expression BRAINLIEST + 18 FOR CORRECT ANSWERHow does the U.S. Constitution ensure that the president does not act outside the rule of law? It creates the requirement that the president must be a natural-born citizen. It gives Congress the ability to remove the president for wrongdoing. It creates a Supreme Court that must pre-approve any presidential action. It gives regular citizens the power of recall elections. i really need help, does anyone know these Why are people charged so much money for food? In this activity, you will learn more about three individuals who played an important role in the Salem witch trialsCotton Mather, Sarah Good, and Anne Putnam. You will read a brief biography about each person and some primary source information related to each person. You will also answer a few questions to evaluate the credibility of the information in each source.Part ACotton Mather was a powerful Boston clergyman whose ideas about witchcraft influenced many of the judges at the trials. You can read this article to learn more about the life of Cotton Mather.Primary resource: In 1689, Mather published Memorable Providences, Relating to Witchcrafts and Possessions, an account of a witchcraft case in Boston. Read an excerpt from the document to get an idea of what Mather thought about witchcraft.Mather calls himself an eyewitness to the event. Do you think eyewitness accounts are always believable? Why or why not? Write your answer in 50 to 75 words. Which sentence would make the BEST thesis statement for a persuasive essay on recycling?A)Recycling is beneficial to the environment.B)Most towns have some type of recycling program,C)My community recycles plastic, glass and aluminim cans.D)My family recycles more aluminum cans than glass each week. Okay so, I know I've already asked something like this but this time it's a question for my growth mindset class,--> brainiest = best answer--> points 100 (50 for each)--> Question:Let's say you want to memorize meanings of words, okay? Which option would be the best and fastest? Explain in two sentences. (At least.)a) Looking over the definitions until you get it.b) Making tools to help you.c) Testing yourself until you get all of them correct.d) (Write your own.) Second Question:How do you study for a spelling test? Let's say it's due tomorrow. (Opinion)a) Keep writing down the words until you get them correct.b) Making tools to help you.c) Memorizing the spelling.d) (Write your own.)Please answer this for me!!! At a school 60% of students buy a school lunch. Only 10% of students buy lunch and dessert. What is the probability that a student who buys lunch also buys dessert? Solve for the variable! 4 questions! Need to turn it in soon so ASAP!Please show your steps! Thank you! When a number is subtracted from -3 2/3 , the result is -2 1/6. What is the number?A.5 5/6B. 1 1/2C. - 1 !/2 D. -5 5/6 A neighbour comes to your door and asks you to feed his dogs, water his plants, and mow his yard while he is out of town for a month. Feeling only slightly guilty, you turn down this large request. Then, the same neighbour returns the next day and asks if you would at least pick up his mail while he is gone. Chances are very good that you will honour this smaller request because of which compliance approach?a. foot-in-the-door technique.b. highball effect.c. lowball technique.d. door-in-the-face effect. PLEASE HELP FAST drag the tiles to the correct boxes to complete the pairs Point U on a graph is located at (4,8), Point V on the same graph is located at (12, 14).Which point lies on Line UV?A. ( 7 , 12 )B. ( 10 , 14 )C. ( 16 , 22 )D. ( 20 , 20 ) 35. John Winthrop's speech reflects which of the following trends?A) The Puritans who settled Massachusetts Bay Colony were mostly like-mindedB) Enlightenment notions of the importance of science and reasonC) Competition between European nations over natural resources in the new worldD) Increasing hostility with Native Americans in New England How happy your last letters have made me those since Christmas Eve! I should like to call you by all the endearing epithets, and yet I can find no lovelier word than the simple word dear, but there is a particular way of saying it. My dear one, then, I have wept for joy to think that you are mine, and often wonder if I deserve you. Which of these is the best definition for the word epithet as it is used in this excerpt? Quote of the day; about me it can help you A school assembly had 600 students in attendance, and 35% of them were first-graders. How many first-graders were at the assembly?can u also list the formula on how to do this while ur at it pls and ty a cell that gains water when it is immersed in a solution is __. put the word s in order to make meaning ful sentence. friend/French/ I/who/a/can/have /speak 30 POINTS!!Use the RACE strategy to answer this question: Why did the Tokugawa Shogunate want to close the borders to Japan? Use pages 161-162 in your Human Odyssey Textbook for the "C" portion of RACE.