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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 54 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.

- 10, - 1

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start factoring the expression!

x^2+11x+10=0
WriteSum

Write as a sum

x^2+x+10x+10=0
â–¼
Factor out x & 10
FactorOut

Factor out x

x(x+1)+10x+10=0
FactorOut

Factor out 10

x(x+1)+10(x+1)=0
FactorOut

Factor out (x+1)

(x+10)(x+1)=0

Solving

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

(x+10)(x+1)=0
ZeroProdProp

Use the Zero Product Property

lcx+10=0 & (I) x+1=0 & (II)
SubEqn

(I): LHS-10=RHS-10

lx=- 10 x+1=0
SubEqn

(II): LHS-1=RHS-1

lx_1=- 10 x_2=- 1

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=- 10.

x^2+11x+10=0
Substitute

x= - 10

( - 10)^2+11( - 10)+10? =0
â–¼
Simplify
CalcPow

Calculate power

100+11(- 10)+10? =0
MultPosNeg

a(- b)=- a * b

100-110+10? =0
AddSubTerms

Add and subtract terms

0=0 ✓

Substituting and simplifying created a true statement, so we know that x=- 10 is a solution of the equation. Let's move on to x=- 1.

x^2+11x+10=0
Substitute

x= - 1

( - 1)^2+11( - 1)+10? =0
â–¼
Simplify
CalcPow

Calculate power

1+11(- 1)+10? =0
MultPosNeg

a(- b)=- a * b

1-11+10? =0
AddSubTerms

Add and subtract terms

0=0 ✓

Again, we created a true statement. x=- 1 is indeed a solution of the equation.

Subchapter links expand_more
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11
Adding and Subtracting Polynomials 12 (Page 81)
Adding and Subtracting Polynomials 13 (Page 81)
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