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Chapter 7: Q. 7.134 (page 876)

Factor completely:

16x2+24xy-4x-6y

Short Answer

Expert verified

The factored form is 2(2x+3y)(4x-1).

Step by step solution

01

Step 1. Given Information  

We are given a polynomial 16x2+24xy-4x-6y,

We have to factor the given polynomial.

02

Step 2. Factoring the polynomial  

Factoring out GCF 2, we get

localid="1647832852748" 16x2+24xy-4x-6y=28x2+12xy-2x-3y

Grouping the terms, we get

16x2+24xy-4x-6y=28x2+12xy+(-2x-3y)16x2+24xy-4x-6y=2(4x(2x+3y)-1(2x+3y))

Factoring out GCF 2x+3y, we get

16x2+24xy-4x-6y=2(2x+3y)(4x-1)

03

Step 3. Checking the factors  

Multiplying the factors, we get

2(2x+3y)(4x-1)=16x2+24xy-4x-6y2(4x(2x+3y)-1(2x+3y))=16x2+24xy-4x-6y28x2+12xy-2x-3y=16x2+24xy-4x-6y16x2+24xy-4x-6y=16x2+24xy-4x-6yLHS=RHS

Hence, the factors are correct.

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