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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 2 Page 68

To factor a perfect square trinomial, the first and last terms have to be perfect squares.

Perfect Square?: No.

Practice makes perfect

To completely factor the given expression, we will first identify the greatest common factor.

Factor Out the GCF

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 6.

6x^2+30x+36

SplitIntoFactors

Split into factors

6(x^2)+ 6(5x)+ 6(6)

Factor out 6

6(x^2+5x+6)

Factor the Trinomial

To determine if an expression is a perfect square trinomial, we need to ask ourselves three questions.

Is the first term a perfect square?	x^2=( x)^2 ✓
Is the last term a perfect square?	6=( sqrt(6))^2 *
Is the middle term twice the product of 6 and x?	5x≠ 2* sqrt(6)* x *

As we can see, the answer to the second and the third questions is no. Therefore, we cannot write the trinomial as the square of a binomial.

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Exercises p.68-71