Chapter 7: Q. 107. (page 832)

In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$a^{2} + 5 a b - 24 b^{2}$

Short Answer

Expert verified

The factorization of $a^{2} + 5 a b - 24 b^{2}$ is $(a + 8 b) (a - 3 b)$

Step by step solution

Step 1. Given information

Given expression is $a^{2} + 5 a b - 24 b^{2}$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

Factors of -24	Sum of factors
8, -3	8 + (-3) = 5
12, -2	12 + (-2) = 10
4, -6	4 + (-6) = -2

Step 3. Factorization

Use $8$ and $- 3$ as the last terms of the trinomials.

$a^{2} + 5 a b - 24 b^{2} = (a + 8 b) (a - 3 b)$

Step 4. Check

$(a + 8 b) (a - 3 b) = a^{2} + 8 a b - 3 a b - 24 b^{2} = a^{2} + 5 a b - 24 b^{2}$

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In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$a^{2} + 5 a b - 24 b^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials.

Step 3. Factorization

Step 4. Check

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In the following exercises, factor each trinomial of the form x2+bxy+cy2a2+5ab-24b2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials.

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Geometry

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$a^{2} + 5 a b - 24 b^{2}$