Factoring Polynomials: Sum and Difference of Cubes Answers
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Which monomial is a perfect cube?
A
1x3B
3x3C
6x3D
9x32
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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)3
Which monomial is a perfect cube?
A
49p9q3r24B
81p12q15r12C
121p9q3r6D
343p6q21r64
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
3B
9C
18D
275
Which expression is equivalent to ?
A
7x3y4z2B
7x3y6z2C
49x3y6z2D
49x3y4z26
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)7
Which is a difference of cubes?
A
x6 – 27B
x15 – 36C
x16 – 64D
x5 – 1258
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)9
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.10
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)Did you find these answers helpful?
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