Chapter 6: Q. 448 (page 638)

Factor completely:
$p^{2} + p q - 12 q^{2}$ .

Short Answer

Expert verified

The factored polynomial is,

$(p + 4 q) (p - 3 q)$ .

Step by step solution

Step 1. Given the information.

The polynomial function is,

$p^{2} + p q - 12 q^{2}$ .

Step 2. Factoring the polynomial.

$p^{2} + p q - 12 q^{2}$

Splitting the middle term such that the sum of the terms is $1$ and the product of the terms is $(- 12)$ .

$= p^{2} + 4 p q - 3 p q - 12 q^{2}$

$= (p^{2} + 4 p q) - (3 p q + 12 q^{2})$

Finding the common factors,

$= p (p + 4 q) - 3 q (p + 4 q) = (p + 4 q) (p - 3 q)$

Step 3. Checking the solution.

$(p + 4 q) (p - 3 q)$

Multiplying the brackets,

$= p (p - 3 q) + 4 q (p - 3 q) = p^{2} - 3 p q + 4 p q - 12 q^{2} = p^{2} + p q - 12 q^{2}$

This is true.

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Factor completely:
$p^{2} + p q - 12 q^{2}$ .

Short Answer

Step by step solution

Step 1. Given the information.

Step 2. Factoring the polynomial.

Step 3. Checking the solution.

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Factor completely:p2+pq-12q2.

Short Answer

Step by step solution

Step 1. Given the information.

Step 2. Factoring the polynomial.

Step 3. Checking the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Discrete Mathematics

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Factor completely:
$p^{2} + p q - 12 q^{2}$ .