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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 61 Page 71

Expand the polynomial using the pattern for a negative perfect square. Then, solve for x.

B

Practice makes perfect

We can begin by expanding the squared term and creating an equation equal to 0.

(x-3)^2=25

ExpandNegPerfectSquare

(a-b)^2=a^2-2ab+b^2

x^2-6x+3^2=25

Calculate power

x^2-6x+9=25

LHS-25=RHS-25

x^2-6x-16=0

Next, we want to factor the new polynomial. We can check for factors by identifying which factors of -16 add up to -6.

Factors of -16	Sum of Factors
-1, 16	15
-2, 8	6
-4, 4	0
1, -16	-15
2, -8	-6

We can use the factors we identified to form the factors of the polynomial. (x+2)(x-8) Finally, we can find the solution by creating an equation equal to 0 for each factor.

Equation	Solution
x+2=0	x=-2
x-8=0	x=8

We can identify that the only choice that matches our answer is option B.

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Exercises p.68-71