g(x) is a polynomial that has a leading coefficient of 3, and the following roots -1,1,2. Write g(x) in standard form

Answers

Answer 1

The standard form of the polynomial is written as:

p(x) = 3*x^3 - 6*x^2 - 3x + 6

How to write the polynomial in standard form?

We know that a polynomial of degree N is with the zeros {x₁, x₂, ...} and a leading coefficient a can be written as:

p(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)

In this case, we know that the leading coefficient is 3, and the zeros of the polynomial are {-1, 1, 2}

Then we can write:

p(x) = 3*(x + 1)*(x - 1)*(x - 2)

Now we need to expand that, we will get:

p(x) = 3*(x + 1)*(x - 1)*(x - 2)

p(x) = 3*(x^2 + 1*x + x*(-1) + 1*(-1))*(x - 2)

p(x) = 3*(x^2 - 1)*(x - 2)

p(x) = 3*(x^3 + x^2*(-2) - x + 2)

p(x) = 3*x^3 - 6*x^2 - 3x + 6

That is the polynomial in standard form.

Learn more about polynomials:

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Related Questions

Write an expression in the form ax+b, where a and b represent rational numbers, that is equivalent to 6 (-1/2x + 2) + 1/4 (18x-12)


I need this answered by today, please!!

Answers

Answer:

[tex]6x + 6[/tex]

Step-by-step explanation:

Given

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12)[/tex]

Required

Express as [tex]ax + b[/tex]

We have:

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12)[/tex]

Open brackets

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 6 *-\frac{1}{2}x + 6*2 + \frac{1}{2} *18x-\frac{1}{2} *12[/tex]

Evaluate all multiplications

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = -3x + 12 + 9x-6[/tex]

Collect like terms

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 9x-3x + 12-6[/tex]

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 6x +6[/tex]

Hence, the expression in form of [tex]ax + b[/tex] is [tex]6x + 6[/tex]

5x-20x+30x. plz help​

Answers

It is going to be 15x if you are trying to simplify it

Answer:

15x

Step-by-step explanation:

5x-20x+30x=15x

answer this please I need a real answer

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

x² + 2x + 1 = 2x² - 2 ( subtract x² + 2x + 1 from both sides

0 = x² - 2x - 3 ← in standard form

0 = (x - 3)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

-----------------------------------

(b)

[tex]\frac{x+2}{3}[/tex] - [tex]\frac{2}{15}[/tex] = [tex]\frac{x-2}{5}[/tex] ( multiply through by 15 to clear the fractions )

5(x + 2) - 2 = 3(x - 2) ← distribute parenthesis on both sides

5x + 10 - 2 = 3x - 6

5x + 8 = 3x - 6 ( subtract 3x from both sides )

2x + 8 = - 6 ( subtract 8 from both sides )

2x = - 14 ( divide both sides by 2 )

x = - 7

--------------------------------------------

(c) Assuming lg means log then using the rules of logarithms

log [tex]x^{n}[/tex] ⇔ nlogx

log x = log y ⇒ x = y

Given

log(2x + 3) = 2logx

log(2x + 3) = log x² , so

x² = 2x + 3 ( subtract 2x + 3 from both sides )

x² - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = 3 , x = - 1

x > 0 then x = 3


Two tanks contain equal amount of liquid. They are connected by a pipe and 2500 gallons is
pumped from tank 1 to tank 2. When the pumping is done, one tank then contains 5 times as
much as the other. How many gallons did each tank contain at the start?

Answers

Answer:

3750

Step-by-step explanation:

Let the tank contain x gallons of water.

when pumping is done, then tank 1 contain x-2500 gallons

and tank 2 contain x+2500 gallons.

according to question,

5(x - 2500) = x + 2500

or, 5x -12500 =x+ 2500

or, 5x - x =2500+12500

or, 4x =15000

or, x= 3750

hence each tank contains 3750 gallons.

Jamie went deep sea diving. If he descends at a rate of 4 feet per minute, what integer represents his depth after 8 minutes?

Answers

Answer: 32 ft.

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

4 feet per minute times 8 minutes equals 32

pls help me on number 1

Answers

Answer:

A. 25in.³

Step-by-step explanation:

Volume of a prism = area of base × height

Please help serious answers only

Answers

Answer:

[tex](-9.5,2.63)[/tex]

Step-by-step explanation:

In essence, this problem asks one to find the vertex of the given equation. An easy way to find the vertex of a quadratic equation in standard form is to complete the square.

Completeting the square involves grouping the quadratic and linear term, then factoring out the coefficient of the quadratic term. After doing so, one will add a term to make the grouped terms a perfect square trinomial and then balance the equation. Finally, one will simplify the equation and get the quadratic equation in vertex form. From there, finding vertex is quite easy, the x-coordinate is the additive inverse of the quadratic term, and the y-coordinate is the constant.

Once a quadratic equation in standard form has been converted to vertex form by the process of completing the square, its equation is amongst the lines of the following,

[tex]a(x-k)^2+h[/tex]

(k, h) is the vertex of the parabola.

The quadratic equation in standard form,

[tex]2x^2+19x+42.5[/tex]

Group the quadratic and linear terms,

[tex](2x^2+19x)+42.5[/tex]

Factor out the coefficient of the quadratic term,

[tex]2(x^2+9.5x)+42.5[/tex]

Add a term to make the grouped part a perfect square trinomial, then balance the equation,

[tex]2(x^2+9.5x+22.5625)+42.5-2(22.5625)[/tex]

Simplify,

[tex]2(x^2+9.5x+22.5626)+42.5-45.125[/tex]

[tex]2(x+9.5)^2+2.625[/tex]

The vertex of the equation is the following,

[tex](-9.5,2.625)[/tex]

Rounded,

[tex](-9.5,2.63)[/tex]

Your carry-on bag can weigh at most 40 pounds.Select an inequality that represents how much more weight x (in pounds) you can add to the bag and seal meet the requirement. Then solve the inequality.

Answers

Answer:

22 + x ≤ 40

x ≤ 18 pounds

Step-by-step explanation:

Maximum weight = 40 pounds

Initial weight = 22 pounds

Let Maximum weight that can be added = x

Mathematically, this means :

Initial weight + additional weight ≤ 40

That is ;

22 + x ≤ 40

Additional weight, x :

x ≤ 40 - 22

x ≤ 18 pounds

A student completed the problem below. Explain in your own words how to verify
if the answer is correct. *
2x^2 – 5x - 3 = (2x + 1)(x - 3)

Answers

Answer:
2x^2 - 5x - 3 = (2x + 1) (x - 3) IS CORRECT

Step-by-step explanation:

F O I L : Firsts Outsides Insides Lasts

— (2x+ 1) (x - 3) Multiply 2x with x = 2x^2

— (2x + 1) (x - 3) Multiply 1 with -3 = -3

— (2x + 1) (x - 3) Multiply -3 with 2x = -5x


(2x + 1) (x - 3) = 2x^2 - 5x - 3

Answer is CORRECT!

Please mark me as brainliest

Can you help me please, no links​

Answers

Answer:

Step-by-step explanation:

x is one-half the value of its intercepted arc. Therefore, x is 110/2 which is 55. Second choice down is the one you want.

Simplify

2/6
——-
2/3

Answers

Answer:

1/2

Step-by-step explanation:

You can change it to multiplication then solve

(2/6)*(3/2)=3/6=1/2

Step-by-step explanation:

You mean

╭☞2/6/2/3?

Ans:-

[tex]╭☞ \sf \: \dfrac{2}{ \dfrac{6}{ \dfrac{2}{3} } } \\ ╭☞ \sf \: \frac{2}{6} \times \frac{3}{2} \\ ╭☞ \sf \: \frac{3}{6} \\ ╭☞ \bf \: \frac{1}{2} [/tex]

A student spent 3 hours on homework last night. What percent of the day was spent on homework?

Answers

Answer:

12.5% of the day

Step-by-step explanation:

There are 24 hours in 1 day

3/24 = 1/8

.125 = 12.5%

Answer:

12.5%

Step-by-step explanation:

Jeff is buying books at a used bookstore. He wants to approximate the total cost of his purchase before checking out. Which amount is the most reasonable approximation of the total price of the 5 books?

Answers

Answer:

35 is a reasonable amount

Step-by-step explanation:

Since all of the books cost around $7 and there are 5 books

when you multiply 7x5=35

PLZ HELP ASAP, LINKS AND ABSURD ANSWERS WILL BE REPORTED! I WILL MARK BRAINLIEST!!

Answers

The closest answer I can see you type is: 35/1.66666666

This is because you divide 21 by 18 which (if you divide 21 by 1.666666 you get 18) and whatever you do to 1 side, you do to the other, then you get 35/1.6666666

3 Simplify 3e - e + 4e

Answers

6e combine like terms

help me with math please

Answers

Answer:

b. 4ft

Step-by-step explanation:

thank you for the points, have an amazing day! :)

Answer:

C.

Step-by-step explanation:

We need to use the Pythagorean theorem to complete this problem. We are given the hypotenuse and the base of the triangle in the middle. The hypotenuse is 5 and the base is 3.[tex]5^{2}[/tex] + [tex]3^{2}[/tex] = [tex]a^{2}[/tex] is what we will complete.

[tex]5^{2} +3^{2} = a^{2}[/tex]

[tex]25 + 9 = 34[/tex]

[tex]34 = a^{2}[/tex]

[tex]\sqrt{34} =a[/tex]

Therefore, the answer is C.

value of 4y when y = -3

Answers

Answer:

-12

Step-by-step explanation:

4y=4*(-3) 4*(-3)=-12

Answer:

It’s -12

Step-by-step explanation:


A(n) is a written agreement between different parties.
A. contract
B. commitment
C. month-to-month
D. annual commitment

Answers

Answer:

A. contract

Step-by-step explanation:

7. What is the interquartile range for the following list of data?
1, 13, 15, 4, 1, 12, 6, 12, 6

Answers

Answer:

10

Step-by-step explanation:

1, 1, 4, 6, 6, 12, 12, 13, 15

[tex]LQ=\frac{9+1}{4} =2.5 term= \frac{1+4}{2}=\frac{5}{2}=2.5\\UQ= 3(\frac{9+1}{4}) =7.5 term= \frac{12+13}{2}=\frac{25}{2}=12.5\\IQR=UQ-LQ=12.5-2.5=10[/tex]

Show me your thinking! This is not for marks but so that I get to know you more as a thinker
Determine the rule and the number of flowers at step 43.

Answers

Answer:

what do you mean

Step-by-step explanation:

can we see step 43

19 Which of the following is equivalent to 2(12-6n+9)- Z(n? - En+9)? =1 19 Ο Σ(n- 32 =10 19 Ο Σ(n-32 19 Ο Σ(n+ 3)? =10 19 Ο Σ(n+ 3)?


EDGE ASAP!!!!​

Answers

Answer:

B if its right i better get brainly list or a follow on ig

Step-by-step explanation:

1nspired_jay

Answer:

Correct answer is A

Step-by-step explanation:

When solving the inital problem you get 1405

Solved problems:

A: 1405

B: 1466

C: 3145

D: 3410

Therefore the correct answer is A

What is the side length of the smaller square plate on which 36 CM chopstick can fit along a diagonal without any overhang

Answers

Step-by-step explanation:

2

57

65

566

77788

66777

66788

67899

6789

78899

789999

88889

8888888

788889

888888999999999

The table shows morgan’s tips from five customers that he served at the Pizza Palace. What percent of these customers left more than a 15% tip? (i really need help PLEASE)

Answers

Answer:

2 people left more than 15%.

A cylinder has a base radius of 3cm and a height of 2cm. What is its volume in cubic
cm, to the nearest tenths place?

Answers

Answer:

V=56.5

Step-by-step explanation:

Formula for finding volume of a cylinder is  V=pi r^2h, substitute h for the height and r for radius. V=pi 3^2 2

NEED HELP ASAP, I WILL GIVE YOU BRAINLIEST

A circle has a radius of 17 ft. Find the length s of the arc intercepted by a central angle of 1.1 radians. Do not round any intermediate computations, and round your answer to the nearest tenth.​

Answers

Answer:

0.9412

Step-by-step explanation:

Ultimately, if you know the length of the arc, and you know the length of the radius, the central angle (in radians) is just how many radii long the arc is. angle=arc lengthradius length=16 feet17 feet≈0.9412.

Please help me with this

Answers

Answer:

Step-by-step explanation:

i think you have to multiply then divide

Use arrow notation to describe the translation of point P(8, –5) to point P'(15, –6).

Answers

Answer:

Step-by-step explanation:

From (-5,-4) to (-8, -7) is left 3 and down 3. In arrow notation: <-3 \/3

figure out what the x and y components of the translation are and then write the arrow to show the direction'

Find the derivative of f(x) = -5 divided by x at x = 11. (5 points)

Answers

AThe chosen topic is not meant for use with this type of problem. Try the examples below.

f (x) = 7x − 2, x = 6

f (x) = 3x − 2, x = 9

f (x) = x^2, x = 12

Answer:

I believe it is 2.2

Step-by-step explanation:

5 goes into 11. 2 times. 2times5= 10 and 11-10=1- 5 goes into 10 2 times- 2 times 5=10; 10-10=0. Therefore it would be 2.2. Hope this helps you. :)

SIMPLIFY (√2 + √5) ²

Answers

Answer:

7+2√10

Step-by-step explanation:

Answer:

7+2√10

Step-by-step explanation:

Which equation best represents the relationship between x and y in the graph?
A. y = 3x + 3
B. y = x + 3
C. y = 3x - 1
D. y = 13 - 1


15 points pls I need ASAP

Answers

Answer:

A. y = 3x + 3

Step-by-step explanation:

y=mx+b

b is the y-intercept (0,y) so lets start with that

We can see that the line touches 3 on the y intercept to get (0,3) meaning b=3

For the slope (m) I like to count rise over run so if we start from (0,3) and go up 3 over 1 we get 3/1 or 3 for m

The whole equation is y=3x+3

the answer is A because the first intercept would be at positive three
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