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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3 Simplify 3e - e + 4e
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)
A student spent 3 hours on homework last night. What percent of the day was spent on homework?
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:
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
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
SIMPLIFY (√2 + √5) ²
Answer:
7+2√10
Step-by-step explanation:
Answer:
7+2√10
Step-by-step explanation:
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.
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
Please help me with this
Answer:
Step-by-step explanation:
i think you have to multiply then divide
5x-20x+30x. plz help
Answer:
15x
Step-by-step explanation:
5x-20x+30x=15x
Please help serious answers only
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]
Find the derivative of f(x) = -5 divided by x at x = 11. (5 points)
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. :)
Use arrow notation to describe the translation of point P(8, –5) to point P'(15, –6).
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'
7. What is the interquartile range for the following list of data?
1, 13, 15, 4, 1, 12, 6, 12, 6
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]
pls help me on number 1
Answer:
A. 25in.³
Step-by-step explanation:
Volume of a prism = area of base × height
answer this please I need a real answer
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
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!!
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]
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?
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
What is the side length of the smaller square plate on which 36 CM chopstick can fit along a diagonal without any overhang
Step-by-step explanation:
2
57
65
566
77788
66777
66788
67899
6789
78899
789999
88889
8888888
788889
888888999999999
Jamie went deep sea diving. If he descends at a rate of 4 feet per minute, what integer represents his depth after 8 minutes?
Answer: 32 ft.
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
4 feet per minute times 8 minutes equals 32
value of 4y when y = -3
Answer:
-12
Step-by-step explanation:
4y=4*(-3) 4*(-3)=-12
Answer:
It’s -12
Step-by-step explanation:
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)
Answer:
2 people left more than 15%.
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.
Answer:
what do you mean
Step-by-step explanation:
can we see step 43
Can you help me please, no links
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
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]
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.
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.
PLZ HELP ASAP, LINKS AND ABSURD ANSWERS WILL BE REPORTED! I WILL MARK BRAINLIEST!!
A(n) is a written agreement between different parties.
A. contract
B. commitment
C. month-to-month
D. annual commitment
Answer:
A. contract
Step-by-step explanation:
help me with math please
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.
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!!!!
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
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?
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
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?
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.