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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Study Guide and Review
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Exercise 52 Page 83

Make sure you rewrite the equation leaving all the terms on one side and that you factor out the greatest common factor if it exists.

- 8, - 4

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start factoring the expression!

x^2+12x+32=0
WriteSum

Write as a sum

x^2+4x+8x+32=0
â–¼
Factor out x & 8
FactorOut

Factor out x

x(x+4)+8x+32=0
FactorOut

Factor out 8

x(x+4)+8(x+4)=0
FactorOut

Factor out (x+4)

(x+8)(x+4)=0

Solving

To solve this equation we will apply the Zero Product Property.

(x+8)(x+4)=0
ZeroProdProp

Use the Zero Product Property

lcx+8=0 & (I) x+4=0 & (II)
SubEqn

(I): LHS-8=RHS-8

lx=- 8 x+4=0
SubEqn

(II): LHS-4=RHS-4

lx_1=- 8 x_2=- 4

Checking Our Answer

 Checking our answer
We can substitute our solutions back into the given equation and simplify to check if our answers are correct. We will start with x=- 8.

x^2+12x+32=0
Substitute

x= - 8

( - 8)^2+12( - 8)+32? =0
â–¼
Simplify
CalcPow

Calculate power

64+12(- 8)+32? =0
MultPosNeg

a(- b)=- a * b

64-96+32? =0
AddSubTerms

Add and subtract terms

0=0 ✓

Substituting and simplifying created a true statement, so we know that x=- 8 is a solution of the equation. Let's move on to x=- 4.

x^2+12x+32=0
Substitute

x= - 4

( - 4)^2+12( - 4)+32? =0
â–¼
Simplify
CalcPow

Calculate power

16+12(- 4)+32? =0
MultPosNeg

a(- b)=- a * b

16-48+32? =0
SubTerms

Subtract terms

0=0 ✓

Again, we created a true statement. x=- 4 is indeed a solution of the equation.

Subchapter links expand_more
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Adding and Subtracting Polynomials 12 (Page 81)
Adding and Subtracting Polynomials 13 (Page 81)
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