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Chapter 6: Q. 347 (page 634)

In the following exercises, factor the greatest common factor from each polynomial.

鈭�3x3+27x2鈭�12x

Short Answer

Expert verified

The factored form of the polynomial is,

3x(-x2+9x-4)

Step by step solution

01

Step 1. Given Information 

We are given a polynomial,

鈭�3x3+27x2鈭�12x

02

Step 2. Finding the greatest common factor

Factoring the polynomial,

3x3==3脳x脳x脳x27x2=3脳3脳3脳x脳x12x=2脳2脳3脳x

The greatest common factor is 3x, so

role="math" localid="1644831720304" 鈭�3x3+27x2鈭�12x=-3x脳x2+3x脳9x-3x脳4鈭�3x3+27x2鈭�12x=3x(-x2+9x-4)

03

Step 3. Checking the factorization 

Multiplying the factors,

3x(-x2+9x-4)=鈭�3x3+27x2鈭�12x鈭�3x3+27x2鈭�12x=鈭�3x3+27x2鈭�12xLHS=RHS

Hence the factorization is correct.

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