Question 1

Which of the following is the greatest common factor (GCF) of the polynomial $6x^3 - 9x^2 + 12x$?

Accepted Answer

$3x$

Question 2

Factor the polynomial $x^2 + 8x + 15$ completely over the integers.

Accepted Answer

$(x + 3)(x + 5)$

Question 3

Which of the following polynomials is irreducible over the integers?

Accepted Answer

$x^2 + 2x + 2$

Question 4

Factor the difference of squares: $49x^2 - 25$.

Accepted Answer

$(7x + 5)(7x - 5)$

Question 5

Which of the following is a perfect square trinomial?

Accepted Answer

$x^2 + 10x + 25$

Question 6

Factor the sum of cubes: $x^3 + 8$.

Accepted Answer

$(x + 2)(x^2 - 2x + 4)$

Question 7

A chemical reaction produces a polynomial $x^3 - 27$. Factor this expression completely.

Accepted Answer

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

Question 8

Factor the polynomial $2x^2 + 10x$ by first finding the GCF.

Accepted Answer

$2x(x + 5)$

Question 9

Which strategy should be used first when factoring any polynomial?

Accepted Answer

Factor out the greatest common factor (GCF)

Question 10

Factor the trinomial $3x^2 - 10x + 8$.

Accepted Answer

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

Question 11

A medical dosage formula is modeled by $x^2 - 16$. Factor this expression to find possible dosages.

Accepted Answer

$(x + 4)(x - 4)$

Question 12

Factor the expression $x^2 - 6x + 9$ and identify its type.

Accepted Answer

$(x - 3)^2$, perfect square trinomial

Question 13

Factor the polynomial $x^3 + 27$ using the sum of cubes formula.

Accepted Answer

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

Question 14

Given the polynomial $x^4 - 16$, which factoring technique should be applied first?

Accepted Answer

Difference of squares

Question 15

Factor the expression $x^2 - 25$ and explain the result.

Accepted Answer

$(x + 5)(x - 5)$, difference of squares

Question 16

Factor the polynomial $x^2 + 12x + 36$ and identify its type.

Accepted Answer

$(x + 6)^2$, perfect square trinomial

Question 17

Factor the expression $(x - 1)^{-\frac{1}{2}}(2x - 1)$ and simplify.

Accepted Answer

$\frac{2x - 1}{(x - 1)^{\frac{1}{2}}}$

Question 18

A polynomial $x^2 + 4x + 4$ models the area of a square garden with an added walkway. Factor the expression to find the side length.

Accepted Answer

$(x + 2)^2$

Question 19

Which of the following is the correct factorization for $x^2 - 2x - 15$?

Accepted Answer

$(x - 5)(x + 3)$

Factoring Polynomials – Fundamental Concepts of Algebra (Precalculus Chapter P.5)

Study Guide - Practice Questions