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

$$ b^2$ - 4c \u003e 0 $$

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

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