AnswersAZ-Common Core Algebra II ASum and Difference of Two Cubes

Factoring Polynomials Completely Answers

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What is the factored form of x3 + 64?

A
(x2 + 8)(x + 8)
B
(x + 4)(x2 – 4x + 16)
C
(x – 4)(x2 + 4x + 16)
3

Factor out the common factor.

A
2x4 + 5x3 – 8x –20
B
(x3 + 4)(–2x – 5)
C
(x3 – 4)(2x + 5)
D
(x3 + 4)(2x + 5)
4

Which expression is equivalent to x6 – 9?

A
(x3)2 – 33
B
(x3)2 – 32
C
(x3)3 – 32
5

This polynomial is an example of a difference of cubes✔ difference of squaresperfect-square trinomialsum of cubes.

A
difference of cubes
B
✔ difference of squares
C
perfect-square trinomial
D
sum of cubes
6

Which expression is equal to the polynomial below?2x4 + 5x3 – 8x – 20

A
x3(2x + 5) + 4(2x – 5)
B
x3(2x + 5) – 4(2x + 5)
C
x3(2x – 5) – 4(2x – 5)
D
x3(2x + 5) + 4(2x + 5)
9

Check all of the possible first steps in factoring a polynomial with four terms.

A
factor out a GCF
B
factor the difference of cubes
C
factor a sum of cubes
D
factor a difference of squares
E
factor a perfect-square trinomial
F
factor by grouping
10

What is the factored form of x6 – 9?

A
(x + 3)(x – 3)
B
(x5 + 3)(x – 3)
C
(x3 + 3)(x2 – 3)
D
(x3 + 3)(x3 – 3)
12

What is the completely factored form of x2y – 2xy – 24y?

A
(xy + 4)(x – 6)
B
xy(x + 4)(x – 6)
C
y(x + 4)(x – 6)
D
y(x + 4)(xy – 6)
14

A polynomial has two terms. Check all of the factoring methods that should be considered.

A
common factor
B
difference of cubes
C
sum of cubes
D
difference of squares
E
perfect-square trinomial
F
factoring by grouping
15

What is the completely factored form of x3 + 4x2 – 9x – 36?

A
(x + 3)(x – 3)
B
(x2 – 9)(x + 4)
C
(x + 3)(x – 3)(x + 4)
D
(x – 3)(x – 3)(x + 4)

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