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Chapter 6: Q 29E (page 572)

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

-2x3+18x2-8x

Short Answer

Expert verified

The simplest polynomial is

2x(9x-x2-4).

Step by step solution

01

Step 1. Given  

A polynomial is given as-2x3+18x2-8x.

02

Step 2. Concept Used.  

First we have to find the GCF (group common factor). Now, rewrite the given polynomial using GCF and apply the distributive property to factor the expression.

03

Step 3. Calculation.  

A polynomial is given as-2x3+18x2-8x

GCF of the polynomial,

2x3=2脳x脳x脳x18x2=2脳3脳3脳x脳x8x=2脳2脳2脳x


04

Step 4. Simplifying the polynomial.  

-2x3+18x2-8x2x(9x-x2-4)


05

Step 5. Check the solution.  

Check by multiplying the factors.

2x(9x-x2-4)=-2x3+18x2-8x

Which holds true.

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