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Chapter 6: Q. 351 (page 634)

In the following exercises, factor by grouping.

x2+7x-3x-21

Short Answer

Expert verified

The factored form of the polynomial is,

x+7x-3

Step by step solution

01

Step 1. Given Information

We are given a polynomial,

x2+7x-3x-21

02

Step 2. Factorizing the polynomial 

Grouping the terms, we get

x2+7x-3x-21=x2+7x-3x+21

Factoring out greatest common factor, we get

x2+7x-3x-21=xx+7-3x+7

Now, again factoring out greatest common factor, we get

x2+7x-3x-21=x+7x-3

03

Step 3. Checking the factorization 

Multiplying the factors,

x+7x-3=x2+7x-3x-21xx-3+7x-3=x2+7x-3x-21x2-3x+7x-21=x2+7x-3x-21x2+7x-3x-21=x2+7x-3x-21LHS=RHS

Hence the factorization is correct.

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