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Chapter 6: Q. 352 (page 634)

In the following exercises, factor by grouping.

4x2-16x+3x-12

Short Answer

Expert verified

The factored form of the polynomial is,

x-44x+3

Step by step solution

01

Step 1. Given Information

We are given a polynomial,

4x2-16x+3x-12

02

Step 2. Factorizing the polynomial 

Grouping the terms, we get

4x2-16x+3x-12=4x2-16x+3x-12

Factoring out greatest common factor, we get

role="math" 4x2-16x+3x-12=4xx-4+3x-4

Now, again factoring out greatest common factor, we get

4x2-16x+3x-12=x-44x+3

03

Step 3. Checking the factorization  

Multiplying the factors,

x-44x+3=4x2-16x+3x-12x4x+3-44x+3=4x2-16x+3x-124x2+3x-16x-12=4x2-16x+3x-124x2-16x+3x-12=4x2-16x+3x-12LHS=RHS

Hence the factorization is correct.

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