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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 169. (page 603)

In the following exercises, factor completely using the perfect square trinomials pattern.
$100 y^{2} - 52 y + 1$

Short Answer

Expert verified

The factor of the trinomial is $(50 y - 1) (2 y - 1)$ .

Step by step solution

01

Step 1. Given information.

Consider the given trinomial.

$100 y^{2} - 52 y + 1$

02

Step 2. Find the product ac.

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

localid="1645547815336" $a = 100, b = - 52, c = 1$

The product $a c$ is

$100 路 1 = 100$

03

Step 3. Split the middle term.

The two numbers whose product is $100$ and add upto $- 52$ are $- 50$ and $- 2$ .

Split the middle term of the trinomial.

$100 y^{2} - 50 y - 2 y + 1$

04

Step 4. Find the factor.

Factor the trinomial by grouping.

$(100 y^{2} - 50 y) - (2 y - 1) 50 y (2 y - 1) - 1 (2 y - 1) (50 y - 1) (2 y - 1)$

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Most popular questions from this chapter

Factor using the 鈥榓c鈥� method:

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