Question 1

Which of the following is the correct factorization of $x^2 - 49$?

Accepted Answer

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

Question 2

Given the expression $4x^2 - 25y^2$, which factoring technique should be used first?

Accepted Answer

Difference of squares

Question 3

Factor the expression $x^2 + 7x + 12$ completely.

Accepted Answer

$ (x + 3)(x + 4) $

Question 4

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

Accepted Answer

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

Question 5

A quadratic $x^2 + bx + c$ has a positive $c$ and a negative $b$. What can you conclude about the factors?

Accepted Answer

Both factors are negative and their sum is negative

Question 6

Factor $2x^2 + 7x + 3$ using the grouping method.

Accepted Answer

$ (2x + 1)(x + 3) $

Question 7

Which of the following is the correct factorization of $x^2 - 36$?

Accepted Answer

$ (x - 6)(x + 6) $

Question 8

If $x^2 + 11x + 24 = 0$, what are the solutions for $x$?

Accepted Answer

$ x = -6, x = -4 $

Question 9

Which of the following is the correct factorization of $5x^2 - 55x$?

Accepted Answer

$ 5x(x - 11) $

Question 10

A chemical reaction's rate is modeled by $t^2 - 16 = 0$. What are the possible values of $t$?

Accepted Answer

$ t = 4, t = -4 $

Question 11

Factor $x^2 - 10x + 25$ completely.

Accepted Answer

$ (x - 5)^2 $

Question 12

Which of the following is the correct factorization of $x^2 + 5x - 24$?

Accepted Answer

$ (x + 8)(x - 3) $

Question 13

A rectangular garden has an area of $x^2 + 7x + 12$ square meters. What are the possible dimensions of the garden?

Accepted Answer

$ (x + 3) $ meters and $ (x + 4) $ meters

Question 14

Factor $x^2 - 2x - 35$ completely.

Accepted Answer

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

Question 15

Which of the following is the correct factorization of $x^2 + 6x + 9$?

Accepted Answer

$ (x + 3)^2 $

Question 16

Solve the equation $|x^2 - 6x| = 0$ by factoring.

Accepted Answer

$ x = 0, x = 6 $

Question 17

Which of the following is the correct factorization of $x^2 - 5x - 24$?

Accepted Answer

$ (x - 8)(x + 3) $

Question 18

A quadratic equation $x^2 + bx + c = 0$ has two real roots. Which condition must be true about $b$ and $c$?

Accepted Answer

$ b^2 - 4c > 0 $

Question 19

Factor $x^2 - 13x + 36$ completely.

Accepted Answer

$ (x - 9)(x - 4) $

Question 20

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

Accepted Answer

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

Factoring Techniques

Study Guide - Practice Questions