Question 1

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

Accepted Answer

$$5x^2 - 11x + 2 = (5x - 1)(x - 2$$)$$

Question 2

What is the value of $$a \cdot c$$ when factoring the trinomial $$5x^2 - 11x + 2$?

Accepted Answer

$$10$$

Question 3

When factoring $$5x^2 - 11x + 2$, which pair of integers adds to -11$ and multiplies to 10$?

Accepted Answer

$$-1$$ and $$-10$$

Question 4

After splitting the middle term, which is the correct grouping for $$5x^2 - 11x + 2$?

Accepted Answer

$$5x^2 - 10x - x + 2$

Question 5

Which of the following is the correct factorization by grouping for $$5x^2 - 10x - x + 2$?

Accepted Answer

$$(5x^2 - 10x) + (-x + 2) = 5x(x - 2) - 1(x - 2$$)$$

Question 6

After factoring by grouping, what is the next step to factor $$5x^2 - 11x + 2$ completely?

Accepted Answer

Factor out the common binomial $$(x - 2) to $$get $$(5x - 1)(x - 2)$$

Question 7

Which of the following trinomials is prime (cannot be factored over the integers)?

Accepted Answer

$$3x^2 + 2x + 7$

Question 8

A chemical reaction's rate is modeled by the quadratic $$5x^2 - 11x + 2$. If x$ represents the concentration, what are the possible concentrations (real solutions) where the rate is zero?

Accepted Answer

$$x = \dfrac{1}{5}$$ and $$x = 2$$

Question 9

If you attempt to factor $$5x^2 - 11x + 2$ and mistakenly use -2$ and -9$ as the pair of numbers, what error have you made?

Accepted Answer

The numbers do not multiply to $$10$$

Question 10

Which step is NOT necessary when factoring $$5x^2 - 11x + 2$?

Accepted Answer

Factoring out the greatest common factor (GCF)

Question 11

A company models its profit with $$5x^2 - 11x + 2$. For what values of x$ does the company break even?

Accepted Answer

$$x = \dfrac{1}{5}$$ and $$x = 2$$

Question 12

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \dfrac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 13

If you factor $$5x^2 - 11x + 2$ as (5x - 1)(x - 2$$)$$, what is the sum of the roots?

Accepted Answer

$$2 + \dfrac{1}{5} = \dfrac{11}{5}$$

Question 14

Which of the following best describes the process of factoring by grouping?

Accepted Answer

Splitting the middle term and grouping terms to factor common binomials

Question 15

If a trinomial $$ax^2 + bx + c$ cannot be factored over the integers, what is it called?

Accepted Answer

Prime

Factoring Trinomials in Precalculus: Step-by-Step Guide

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