Question 1

Which of the following is the correct factorization of $21x^2 - 41x + 10$?

Accepted Answer

$(3x - 5)(7x - 2)$

Question 2

A trinomial $ax^2 + bx + c$ is factored as $(mx + n)(px + q)$. Which of the following statements is always true?

Accepted Answer

$a = m \cdot p$

Question 3

Which of the following trinomials is a perfect square trinomial?

Accepted Answer

$x^2 + 12x + 36$

Question 4

What is the greatest common factor (GCF) of $3x^3 + 17x^2 + 10x$?

Accepted Answer

$x$

Question 5

Which of the following is the correct factorization of $25x^2 + 20x + 4$?

Accepted Answer

$(5x + 2)^2$

Question 6

A chemist is mixing two solutions, and the concentration of a chemical in the mixture is modeled by $3x^2 - 7x + 6$. Can this trinomial be factored over the integers?

Accepted Answer

No, it is a prime polynomial.

Question 7

Which of the following is the correct factorization of $16x^2 - 8xy + y^2$?

Accepted Answer

$(4x - y)^2$

Question 8

Given the trinomial $ax^2 + bx + c$, which of the following must be true for it to be a perfect square trinomial?

Accepted Answer

$b^2 = 4ac$

Question 9

A medical researcher models the growth of bacteria with the polynomial $x^2 + 6x + 9$. What is the factored form?

Accepted Answer

$(x + 3)^2$

Question 10

Which of the following is the correct factorization of $3x^2 + 17x + 10$?

Accepted Answer

$(3x + 2)(x + 5)$

Question 11

Which of the following trinomials is NOT factorable over the integers?

Accepted Answer

$3x^2 - 7x + 6$

Question 12

A company’s profit is modeled by $x^2 - 12x + 36$. What is the factored form, and what does it tell you about the break-even point?

Accepted Answer

$(x - 6)^2$; the company breaks even when $x = 6$

Question 13

Which of the following is the correct factorization of $a^2 - 2ab + b^2$?

Accepted Answer

$(a - b)^2$

Question 14

If a trinomial $ax^2 + bx + c$ is a perfect square trinomial, which of the following is a possible value for $b$ if $a = 4$ and $c = 9$?

Accepted Answer

$b = 12$ or $b = -12$

Question 15

Which of the following is the correct factorization of $m^2 - 4m + 4$?

Accepted Answer

$(m - 2)^2$

Question 16

A quadratic trinomial $ax^2 + bx + c$ is factored as $(px + q)^2$. Which of the following must be true?

Accepted Answer

$a = p^2$, b = 2pq, c = q^2$

Question 17

Which of the following is the correct factorization of $x^2 + 17x + 16$?

Accepted Answer

$(x + 1)(x + 16)$

Question 18

A trinomial $ax^2 + bx + c$ is factored as $(3x - 5)(7x - 2)$. What is the value of $b$?

Accepted Answer

$-41$

Question 19

Which of the following is the correct factorization of $x^2 - 2x + 1$?

Accepted Answer

$(x - 1)^2$

Question 20

A trinomial $ax^2 + bx + c$ is said to be prime if:

Accepted Answer

It cannot be factored over the integers.

6.3 Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards