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Chapter 7: Q. 289 (page 878)

In the following exercises, factor completely.

8m2-32

Short Answer

Expert verified

The factored form of the polynomial is8m2-32=8(m-2)(m+2).

Step by step solution

01

Step 1. Given Information.  

The given Polynomial is8m2-32.

02

Step 2. Factoring by the difference of square formula.

Terms of a polynomial have a common factor8.

8m2-32=8(m2-4)

In the parentheses, it is a binomial of the difference of square.

factorize it by using the formula of difference of square.

8m2-32=8(m2-4)8m2-32=8(m2-22)8m2-32=8(m-2)(m+2)

Now polynomial cannot be factored further.

So factored form islocalid="1647945020797" 8m2-32=8(m-2)(m+2).

03

Step 3. Verification.  

Check whether the expanded form of the factored polynomial is equal to the original polynomial or not.

8m2-32=?8(m-2)(m+2)8m2-32=?8(m2+2m-2m-22)8m2-32=?8(m2-4)8m2-32=8m2-32

The left-hand side is equal to the right-hand side so factored form is correct.

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