Chapter 7: Q. 7.136 (page 877)

Factor completely:
$6 q^{2} - 9 q - 6$

Short Answer

Expert verified

The factored form is $3 (q - 2) (2 q + 1)$ .

Step by step solution

Step 1. Given Information

We are given a polynomial $6 q^{2} - 9 q - 6$ ,

We have to factor the given polynomial.

Step 2. Factoring the polynomial

Factoring out GCF $3$ , we get

$6 q^{2} - 9 q - 6 = 3 (2 q^{2} - 3 q - 2)$

Using middle terms splitting or acmethod, we get

$6 q^{2} - 9 q - 6 = 3 (2 q^{2} - 4 q + q - 2)$

Grouping the terms, we get

$6 q^{2} - 9 q - 6 = 3 ((2 q^{2} - 4 q) + (q - 2)) 6 q^{2} - 9 q - 6 = 3 (2 q (q - 2) + 1 (q - 2))$

Factoring out GCF $q - 2$ , we get

$6 q^{2} - 9 q - 6 = 3 (q - 2) (2 q + 1)$

Step 3. Checking the factors

Multiplying the factors, we get

$3 (q - 2) (2 q + 1) = 6 q^{2} - 9 q - 6 3 (2 q (q - 2) + 1 (q - 2)) = 6 q^{2} - 9 q - 6 3 (2 q^{2} - 4 q + q - 2) = 6 q^{2} - 9 q - 6 3 (2 q^{2} - 3 q - 2) = 6 q^{2} - 9 q - 6 6 q^{2} - 9 q - 6 = 6 q^{2} - 9 q - 6 L H S = R H S$

Hence, the factors are correct.

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Factor completely:
$6 q^{2} - 9 q - 6$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring the polynomial

Step 3. Checking the factors

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Factor completely:6q2-9q-6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring the polynomial

Step 3. Checking the factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Probability and Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Factor completely:
$6 q^{2} - 9 q - 6$