Question 1

Which of the following is the correct first step when factoring the trinomial $$6x^2 - 2x - 20$ by grouping?

Accepted Answer

Factor out the greatest common factor, which is $$2.$$

Question 2

Given the trinomial $$8x^2 - 14x + 5$, what two numbers should you find to split the middle term when factoring by grouping?

Accepted Answer

$$-4$$ and $$-10$$

Question 3

After factoring out the greatest common factor from $$6x^2 - 2x - 20$, what is the resulting trinomial to factor?

Accepted Answer

$$3x^2 - x - 10$

Question 4

Which of the following is the correct factorization of $$2x^2 + 9x + 4$ by grouping?

Accepted Answer

$$(2x + 1)(x + 4)$$

Question 5

What is the value of $$ac$$ for the trinomial $$8x^2 + 10x - 3$?

Accepted Answer

$$-24$$

Question 6

Which of the following correctly describes the grouping method for factoring trinomials of the form $$ax^2 + bx + c$ where a$$ 
eq 1$$?

Accepted Answer

Split the middle term into two terms whose coefficients add to $$b$$ and whose product is $$ac$$, then factor by grouping.

Question 7

A chemical company needs to factor $$8x^2 - 14x + 5$ to determine the dimensions of a rectangular tank. What are the dimensions in terms of x$?

Accepted Answer

$$(2x - 1)$$ and $$(4x - 5)$$

Question 8

If you are given $$3x^2 - x - 10$, which two numbers multiply to -30$ and add to -1$?

Accepted Answer

$$-6$$ and $$5$$

Question 9

Which of the following is the correct factorization of $$8x^2 + 10x - 3$ by grouping?

Accepted Answer

$$(2x + 3)(4x - 1)$$

Question 10

A medical researcher is modeling the spread of a virus with the equation $$2x^2 + 9x + 4 = 0$. What are the factors of the left side, and what do they represent in this context?

Accepted Answer

$$(2x + 1)(x + 4)$$; they represent possible time intervals and infection rates where the spread is zero.

Question 11

Which step is NOT part of the grouping method for factoring trinomials of the form $$ax^2 + bx + c$?

Accepted Answer

Use the quadratic formula to find the roots.

Question 12

A rectangular garden has an area given by $$6x^2 - 2x - 20$. If the width is (x - 2$$)$$, what is the length?

Accepted Answer

$$2(3x + 5)$$

Question 13

When factoring $$8x^2 + 10x - 3$ by grouping, which of the following is the correct way to rewrite the middle term?

Accepted Answer

$$12x - 2x$$

Question 14

Which of the following trinomials can be factored by grouping into $$(x - 2)(3x + 5)$$?

Accepted Answer

$$3x^2 - x - 10$

Question 15

A business is modeling profit with $$8x^2 - 14x + 5$. If the profit is zero, what are the possible values of x$?

Accepted Answer

$$x = \frac{1}{2} or$$ $$x = \frac{5}{4}$$

Question 16

Which of the following is the correct factorization of $$2x^2 + 9x + 4$ by grouping?

Accepted Answer

$$(2x + 1)(x + 4)$$

Question 17

If a trinomial $$ax^2 + bx + c$ has a = 3$, b = -1$, and c = -10$, what is the value of ac$ and what does it represent in the grouping method?

Accepted Answer

$$ac = -30$$; it is the product used to find two numbers whose sum is $$b$$ and product is $$ac.$$

6.4 Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards