Question 1

Which of the following is the greatest common factor (GCF) of the polynomial $9y^4 + y^2$?

Accepted Answer

$y^2$

Question 2

Factor the polynomial $6x^2 + 8x - 12x$ completely.

Accepted Answer

$2x(3x + 4 - 6)$

Question 3

Which of the following is the correct factorization by grouping for $mp^2 + 7m + 3p^2 + 21$?

Accepted Answer

$(mp^2 + 7m) + (3p^2 + 21)$

Question 4

Given the trinomial $4y^2 - 11y + 6$, which of the following is its correct factorization?

Accepted Answer

$(4y - 3)(y - 2)$

Question 5

Which of the following is the correct factorization for the difference of squares $a^2 - b^2$?

Accepted Answer

$(a + b)(a - b)$

Question 6

Factor the binomial $x^3 + 27$ completely.

Accepted Answer

$(x + 3)(x^2 - 3x + 9)$

Question 7

Which of the following is the correct factorization for $m^3 - 64n^3$?

Accepted Answer

$(m - 4n)(m^2 + 4mn + 16n^2)$

Question 8

A polynomial is considered prime when:

Accepted Answer

It cannot be factored into polynomials of lower degree with integer coefficients.

Question 9

Which of the following is the correct factorization for $16p^2 - 40pq + 25q^2$?

Accepted Answer

$(4p - 5q)^2$

Question 10

Factor the expression $12x^{-2} - 8x^{-3}$ by factoring out the least power of $x$.

Accepted Answer

$4x^{-3}(3x - 2)$

Question 11

Which of the following is the correct factorization for $y^3 - x^3 + 6x - 9$?

Accepted Answer

$(y - x)(y^2 + yx + x^2) + 3(x - 3)$

Question 12

Which of the following is the correct factorization for $x^2 + 13x - 18$?

Question 13

Which of the following is the correct factorization for $36x^2y^2 + 84xy + 49$?

Accepted Answer

$(6xy + 7)^2$

Question 14

Which of the following is the correct factorization for $(2a - 1)^2 + 8$?

Accepted Answer

$(2a - 1 + 2	ext{i}\sqrt{2})(2a - 1 - 2	ext{i}\sqrt{2})$

Question 15

Which of the following is the correct factorization for $4a^2 - 9$?

Accepted Answer

$(2a + 3)(2a - 3)$

Question 16

Which of the following is the correct factorization for $x^2 - 6x + 9 - y^4$?

Accepted Answer

$(x - 3)^2 - y^4$

Question 17

Which of the following is the correct factorization for $6x^4 - 13x^2 - 5$?

Accepted Answer

$(6x^2 + 1)(x^2 - 5)$

Question 18

Which of the following is the correct factorization for $8q^4 + 125p^3$?

Accepted Answer

$(2q^2 + 5p)(4q^4 + 10q^2p + 25p^2)$

Question 19

Which of the following is the correct factorization for $4m^{1/2} + 3m^{3/2}$?

Accepted Answer

$m^{1/2}(4 + 3m)$

Factoring Polynomials in College Algebra: Methods and Applications

Study Guide - Practice Questions