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Chapter 6: Q. 255 (page 613)

In the following exercises, factor completely.

4x2+40x+84

Short Answer

Expert verified

The required factors are4(x+3)(x+7)

Step by step solution

01

Step 1. Given Information

The given expression is4x2+40x+84

02

Step 2. Calculation

We will find the factors by taking common factor out and then use the middle term splitting method.

4x2+40x+84=4(x2+10x+21)=4(x2+7x+3x+21)=4(x(x+7)+3(x+7))=4(x+3)(x+7)

03

Step 3. Check

We will verify the factors by multiplying the factors.

4(x+3)(x+7)=4(x(x+7)+3(x+7))=4(x2+7x+3x+21)=4(x2+10x+21)=4x2+40x+84

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