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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q 170. (page 603)

In the following exercises, factor completely using the perfect square trinomials pattern.
$64 m^{2} - 34 m + 1$

Short Answer

Expert verified

The factor of the trinomial is $(32 m - 1) (2 m - 1)$ .

Step by step solution

01

Step 1. Given information.

Consider the given trinomial.

$64 m^{2} - 34 m + 1$

02

Step 2. Find the product ac.

Compare the given trinomial with $a x^{2} + b x + c$

$a = 64, b = - 34, c = 1$

The product $a c$ is,

$64 路 1 = 64$

03

Step 3. Split the middle term.

The two numbers whose product is $64$ and add up to $- 34$ are $- 32$ and $- 2$ .

Split the middle term of the trinomial.

$64 m^{2} - 32 m - 2 m + 1$

04

Step 4. Find the factor.

Factor the trinomial by grouping.

$(64 m^{2} - 32 m) - (2 m - 1) 32 m (2 m - 1) - 1 (2 m - 1) (32 m - 1) (2 m - 1)$

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Most popular questions from this chapter

Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error.

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