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

Guida di studio - Domande di pratica

Study guide - Flashcard