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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 33 Page 86

The formula to factor the difference of two squares is a^2-b^2=(a+b)(a-b).

G

Look closely at the expression x^4-1. It can be expressed as the difference of two squares.

x^4-1

a^(m* n)=(a^m)^n

(x^2)^2-1

Write as a power

(x^2)^2-1^2

Recall the formula to factor a difference of squares.

a^2- b^2 ⇔ ( a+ b)( a- b) We can apply this formula to our expression. ( x^2)^2- 1^2 ⇔ ( x^2+ 1)( x^2- 1) We can notice that the second factor is also a difference of two squares. Let's use the formula once again. (x^2+1)( x^2- 1) ⇕ (x^2+1)( x+ 1)( x- 1) Now, the given polynomial is completely factored. Therefore, the correct option is G.

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