Question 1

Which of the following is the correct factorization of $$x^2 - 8x + 15$?

Accepted Answer

Question 2

A chemical engineer is designing a container whose area is modeled by $$x^2 + 10x - 24$. To find possible dimensions, factor the trinomial.

Accepted Answer

$$(x + 12)(x - 2)$$

Question 3

Which of the following trinomials is prime (cannot be factored using integer coefficients)?

Accepted Answer

$$x^2 + 2x + 5$

Question 4

A company wants to maximize the area of a rectangular garden with a fixed perimeter. If the area is given by $$x^2 + 9x + 8$, what are the possible dimensions of the garden?

Accepted Answer

$$(x + 8)(x + 1)$$

Question 5

Factor the trinomial $$3x^2 - 2x - 5$ using the grouping method.

Accepted Answer

$$(3x + 5)(x - 1)$$

Question 6

A biologist is modeling population growth with the equation $$6x^2 + 7x + 2$. What is the correct factorization?

Accepted Answer

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

Question 7

Which of the following is the correct first step when factoring $$3x^3$$ + $$24x^2 + 48x$?

Accepted Answer

Factor out the greatest common factor, $$3x$$

Question 8

Factor $$12x^2 - 17x - 5$ completely.

Accepted Answer

$$(4x + 1)(3x - 5)$$

Question 9

A physics problem involves the expression $$-t^2 + 2t + 8$. What is its factorization?

Accepted Answer

$$-(t - 4)(t + 2)$$

Question 10

Which of the following is the correct factorization of $$2x^2 + 11x + 5$?

Accepted Answer

$$(2x + 1)(x + 5)$$

Question 11

A business's profit is modeled by $$5x^2 + 10x + 35$. What is the correct factorization?

Accepted Answer

$$5(x^2 + 2x + 7$$)$$

Question 12

Factor $$20x^2 - 46x + 24$ completely.

Accepted Answer

$$2(2x - 3)(5x - 4)$$

Question 13

Which of the following is the correct factorization of $$x^2 + 15 - 16x$?

Accepted Answer

$$(x - 1)(x - 15)$$

Question 14

A medical researcher is analyzing the expression $$3a^2 + 10a + 7$. What is its factorization?

Accepted Answer

$$(3a + 7)(a + 1)$$

Question 15

Factor $$6x^2 + 5x - 6$ completely.

Accepted Answer

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

Question 16

Which of the following is the correct factorization of $$x^2 + 12x + 13$?

Accepted Answer

$$(x + 1)(x + 13)$$

Question 17

A factory's production is modeled by $$3p^2 - 9p - 120$. What is the correct factorization?

Accepted Answer

$$3(p + 8)(p - 5)$$

Question 18

Which of the following is the correct factorization of $$x^2 + 10x + 25$?

Accepted Answer

$$(x + 5)^2$

Question 19

A student is asked to factor $$48 - 2y - y^2$. What is the correct factorization?

Accepted Answer

$$-(y + 8)(y - 6)$$

Question 20

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

Accepted Answer

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

Factoring Trinomials in Intermediate Algebra

Study Guide - Practice Questions

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