Q. 362 In the following examples, facto... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 362 (page 635)

In the following examples, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$p^{2} - 5 p q - 36 q^{2}$

Short Answer

Expert verified

The factors of the polynomial $p^{2} - 5 p q - 36 q^{2}$ is $(p + 4 q) (p - 9 q)$

Step by step solution

Step 1. Given

The trinomial is $p^{2} - 5 p q - 36 q^{2}$

To find the factors of the trinomial.

Step 2. Write binomial with first term p and second term q

The binomial contains $p$ in the first term and $q$ in the second term.

The last and second term of the binomial is negative, so the factors must have opposite signs with greater number having negative sign.

$p^{2} - 5 p q - 36 q^{2} = (p + q) (p - q)$

Step 3. Find numbers multiply to -36 and add to -5

Find the numbers multiply to $- 36$ and add to $- 5$ .

Factors of $- 36$	Sum of factors
$1, - 36$	$- 35$
$2, - 18$	$- 16$
$3, - 12$	$- 9$
$4, - 9$	$- 5$

Step 4. Find the factors

Use $4, - 9$ as coefficients of last term

$p^{2} - 5 p q - 36 q^{2} = (p + 4 q) (p - 9 q)$

Step 5. Check the answer

The factors are $(p + 4 q) (p - 9 q)$

Multiply the factors

$(p + 4 q) (p - 9 q) = p^{2} - 9 p q + 4 p q - 36 q^{2}$

$= p^{2} - 5 p q - 36 q^{2}$

Hence the multiplication of factors gives the trinomial.

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91影视

In the following examples, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$p^{2} - 5 p q - 36 q^{2}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Write binomial with first term p and second term q

Step 3. Find numbers multiply to -36 and add to -5

Step 4. Find the factors

Step 5. Check the answer

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91影视

In the following examples, factor each trinomial of the form x2+bxy+cy2p2-5pq-36q2

Short Answer

Step by step solution

Step 1. Given

Step 2. Write binomial with first term p and second term q

Step 3. Find numbers multiply to -36 and add to -5

Step 4. Find the factors

Step 5. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Applied Mathematics

Pure Maths

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following examples, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$p^{2} - 5 p q - 36 q^{2}$