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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

Mid-Chapter Quiz

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Exercise 10 Page 224

Is there a greatest common factor (GCF) between all of the terms in the given expression? If so, you should factor that out first.

2(8-m^2)

Practice makes perfect

The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 2.

16-2m^2

SplitIntoFactors

Split into factors

2* 8- 2* m^2

Factor out 2

2(8-m^2)

Looking at the expression 8-m^2, we can see that we could use the formula for factoring the difference of two squares a^2 -b^2 =(a+b)(a-b) However, 8 is not a perfect square, so let's finish factoring the expression here.

Extra

Continuation

In case you would like to see how to factor the given expression further, we included the process below.

2(8-m^2 )

Rewrite 8 as 4* 2

2(4* 2-m^2 )

Write as a power

2( 2^2* (sqrt(2))^2 -m^2)

a^m* b^m=(a * b)^m

2( (2*sqrt(2))^2 -m^2)

Multiply

2( (2sqrt(2))^2 -m^2)

Now we can apply the formula to factor a difference of squares. 2( ( 2sqrt(2))^2 -m^2) ⇕ 2( 2sqrt(2)+m)( 2sqrt(2)-m)