Chapter 11: Q 32 (page 1069)

In the following exercises, factor the greatest common factor from each polynomial.
$- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2}$

Short Answer

Expert verified

The given polynomial is factored as $- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2} = - 6 a b (a^{2} + 2 a b - 3 b)$

Step by step solution

Step 1. Given Information

Consider a polynomial $- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2}$ .

The objective is to factor the polynomial by factoring the greatest common factor.

Step 2. Factor the GCF

The GCF of three terms of the polynomial $- 6 a^{3} b, - 12 a^{2} b^{2}, 18 a b^{2}$ is $- 6 a b$ . So rewriting the polynomial terms with the product of GCF and then using the distributive property we get

$\begin{array}{rcl} - 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2} & = & - 6 a b \cdot a^{2} - 6 a b \cdot 2 a b + (- 6 a b) (- 3 b) \\ = & - 6 a b (a^{2} + 2 a b - 3 b) \end{array}$

Step 3. Check

To check we multiply the factors and we get

$\begin{array}{rcl} - 6 a b (a^{2} + 2 a b - 3 b) & = & - 6 a b \cdot a^{2} + (- 6 a b) \cdot 2 a b + (- 6 a b) (- 3 b) \\ = & - 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2} \end{array}$

And we get the given polynomial. So the factor is done correctly.

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In the following exercises, factor the greatest common factor from each polynomial.
$- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the GCF

Step 3. Check

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In the following exercises, factor the greatest common factor from each polynomial.-6a3b-12a2b2+18ab2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the GCF

Step 3. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Calculus

Pure Maths

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, factor the greatest common factor from each polynomial.
$- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2}$