AnswersCommon Core Algebra I B-ICFactoring Polynomials: Sum and Difference of Cubes

Factoring Polynomials: Sum and Difference of Cubes Answers

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What is the factorization of 729x15 + 1000?

A
(9x5 + 10)(81x10 – 90x5 + 100)
B
(9x5 + 10)(81x5 – 90x10 + 100)
C
(9x3 + 10)(81x6 – 90x6 + 100)
D
(9x3 + 10)(81x9 – 90x3 + 100)
2
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What is the cube root of 27x18?

A
3x6
B
3x9
C
9x6
D
9x9
3

What is the cube root of 64x12?

A
4x4
B
4x6
C
8x4
D
8x6
4

Which expression is equivalent to ?

Question illustration
A
6xy2z4
B
18xy3z6
C
36xy2z4
D
72xy3z6
6

Which is the factorization of x3 + 8?

A
(x + 2)(x2 – 2x + 4)
B
(x – 2)(x2 + 2x + 4)
C
(x + 2)(x2 – 2x + 8)
D
(x – 2)(x2 + 2x + 8)
7

The factorization of 8x3 – 125 is (2x – 5)(jx2 + kx + 25). What are the values of j and k?

A
j = 6 and k = –10
B
j = 8 and k = 10
C
j = 4 and k = 25
D
j = 4 and k = 10
8

Which product will result in a sum or difference of cubes?

A
(x + 7)(x2 – 7x + 14)
B
(x + 8)(x2 + 8x + 64)
C
(x – 9)(x2 + 9x + 81)
D
(x – 10)(x2 – 10x + 100)
9

Hank’s teacher asked him to verify that the product (y−3)(y2+3y+9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3+3y2+ay−3y2−ay−27. What is the value of a in the polynomial?

A
3
B
9
C
18
D
27
10

Which number in the monomial 215x18y3z21 needs to be changed to make it a perfect cube?

A
3
B
18
C
21
D
215
11

Which expression is equivalent to ?

Question illustration
A
7x3y4z2
B
7x3y6z2
C
49x3y6z2
D
49x3y4z2
12

Which monomial is a perfect cube?

A
49p9q3r24
B
81p12q15r12
C
121p9q3r6
D
343p6q21r6
13

What is the factorization of 216x12 – 64?

A
(6x3 – 4)(36x6 + 24x3 + 16)
B
(6x3 – 4)(36x9 + 24x3 + 16)
C
(6x4 – 4)(36x8 + 24x4 + 16)
D
(6x4 – 4)(36x12 + 24x4 + 16)
14

A and B are monomials where A = 125 and B = 27p12. What is the factored form of A – B?

A
(5 – 3p4)(25 + 15p4 + 9p8)
B
(25 – 3p4)(5 + 15p3 + 9p3)
C
(25 – 3p4)(5 + 15p4 + 3p8)
D
(5 – 3p4)(25 + 15p3 + 3p4)
15

Which statements are true about a perfect cube monomial and its roots? Check all that apply.

A
A perfect cube monomial must have exponents on the variables.
B
A perfect cube monomial must have three identical roots, such that the product of the roots equal the perfect square monomial.
C
The coefficient of the monomial must be divisible by 3.
D
Any monomial can be a perfect cube root.
E
The least common multiple of all the exponents on variables of a perfect cube monomial must be 3.
F
It must be possible for the coefficient of a perfect cube monomial to be written in the form n3, where n equals the cube root of the coefficient.
16

Which is a sum of cubes?

A
a3 + 18
B
a6 + 9
C
a9 + 16
D
a12 + 8

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