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Chapter 6: Q. 272 (page 565)

In the following exercises, factor completely(4x-5)2-7(4x-5)+12

Short Answer

Expert verified

The factored form is4(4x-9)(x-2)

Step by step solution

01

Given information

Given the equation(4x-5)2-7(4x-5)+12

02

Multiplying binomial

Multiplying the binomial, we get

(4x-5)2-7(4x-5)+12=16x2-40x+25-28x+35+12=16x2-68x+72=44x2-17x+18=44x2-8x-9x+18=4(4x(x-2)-9(x-2))=4(4x-9)(x-2)

03

Checking the expression

Checking, we get

4(4x-9)(x-2)=44x2-8x-9x+18=44x2-17x+18=16x2-68x+72=16x2-40x+25-28x+35+12=(4x-5)2-7(4x-5)+12

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