Factoring Polynomials: Sum and Difference of Cubes

Question 1

What is the factorization of 216x12 – 64?

Revolt · Accepted Answer

(6x4 – 4)(36x8 + 24x4 + 16)

Question 2

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

Revolt · Accepted Answer

215

Question 3

Which is a difference of cubes?

Revolt · Accepted Answer

x6 – 27

Question 4

Which monomial is a perfect cube?

Revolt · Accepted Answer

343p6q21r6

Question 5

What is the factorization of 729x15 + 1000?

Revolt · Accepted Answer

(9x5 + 10)(81x10 – 90x5 + 100)

Question 6

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

Revolt · Accepted Answer

(x – 9)(x2 + 9x + 81)

Question 7

What is the cube root of 64x12?

Revolt · Accepted Answer

4x4

Question 8

Which statements are true about a perfect cube monomial and its roots? Check all that apply.A perfect cube monomial must have exponents on the variables.A perfect cube monomial must have three identical roots, such that the product of the roots equal the perfect square monomial.The coefficient of the monomial must be divisible by 3.Any monomial can be a perfect cube root.The least common multiple of all the exponents on variables of a perfect cube monomial must be 3.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.

Revolt · Accepted Answer

A perfect cube monomial must have exponents on the variables.; Any monomial can be a perfect cube root.; 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.

Question 9

What is 125x9 + 64y12 written as a sum of cubes?

Revolt · Accepted Answer

(5x3)3 + (4y4)3

Question 10

What is the cube root of 27x18?

Revolt · Accepted Answer

3x6

Factoring Polynomials: Sum and Difference of Cubes Answers

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