1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Murljashka [212]
3 years ago
7

What polynomial expressions equal 8x^3+64?

Mathematics
1 answer:
Natali5045456 [20]3 years ago
6 0

Answer:

\displaystyle \boxed{8[x + 2][x^2 - 2x + 4]}

Step-by-step explanation:

Use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] to figure this out:

\displaystyle 8x^3 + 64 \\ 8[x^3 + 8] \\ \\ x + 2 = \sqrt[3]{x^3 + 8}

Then, since the divisor\factor is in the form of <em>x - c</em>, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

−2| 1 0 0 8

↓ −2 4 −8

___________

1 −2 4 0 → {x}^{2} - 2x + 4

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x³ + 8]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the −2x follows right behind it, then 4, giving you the other factor of x^2 - 2x + 4, attaching this to the first two factors you started out your work on:

\displaystyle \boxed{8[x + 2][x^2 - 2x + 4]}

I am joyous to assist you anytime.

You might be interested in
Mia is "helping" her mom pick up 27 toys that are strewn on the floor. Mia's mom puts five toys into the toy box every 40 second
dedylja [7]

Answer:

8 min

Step-by-step explanation:fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff :)

5 0
2 years ago
Find the volume of prism when following measurements are applied​
astraxan [27]

Answer:

I'm pretty sure its 228

Step-by-step explanation:

I'm sorry if I'm wrong

3 0
3 years ago
joe is playing a game with a regular die. If the number that turns up is even he will gain 5 times the number that comes up. If
vladimir1956 [14]

Answer:

he lost 30 points.

since he rolled an odd number, he will lose 10 times the number he rolled. he rolled 3, which means he lost 30 points. you get that by multiplying 3 and 10.

5 0
3 years ago
Find the missing length <br> answer choices<br>a. 20.2 ft<br>b. 7.5ft<br>c. 11.7ft<br>d. 17.3​
grigory [225]
7.5 ft beacuse it is long
6 0
3 years ago
Read 2 more answers
During a research​ experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At
Sergeeva-Olga [200]
During a research​ experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 8​:00 AM there were 6,000
3 0
3 years ago
Other questions:
  • What type of polynomial is: 2x - 4x<br> - 7+ 6x2
    7·1 answer
  • (2^n)^1/2=64 find value of n
    8·1 answer
  • Factor 18 out of 18x−498 ( THIS IS 7th GRADE MATH BTWWWW &lt;3)
    5·1 answer
  • The 38,483 employees at a manufacturing company must attend a meeting about finances. The meeting room holds 315 people. How man
    11·1 answer
  • The point p(-3,2) is translated up 3 and right 4. what are the coordinates of p
    9·1 answer
  • What is the area of the rectangle whose length is (x + 5) and width (x-5)​
    5·2 answers
  • A chocolate maker melts three blocks of chocolate weighing 5.4 ounces, 6.1 ounces, and 5.7 ounces. If
    5·1 answer
  • HELP PLS :D
    5·1 answer
  • HURRY I NEED THIS BEFORE 12
    11·1 answer
  • Write an equation for the polynomial graphed below
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!