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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
Study Guide and Review
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Exercise 53 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, - 6

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start factoring the expression!

x^2-2x-48=0
WriteDiff

Write as a difference

x^2+6x-8x-48=0
â–¼
Factor out x & - 8
FactorOut

Factor out x

x(x+6)-8x-48=0
FactorOut

Factor out - 8

x(x+6)-8(x+6)=0
FactorOut

Factor out (x+6)

(x-8)(x+6)=0

Solving

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

(x-8)(x+6)=0
ZeroProdProp

Use the Zero Product Property

lcx-8=0 & (I) x+6=0 & (II)
AddEqn

(I): LHS+8=RHS+8

lx=8 x+6=0
SubEqn

(II): LHS-6=RHS-6

lx_1=8 x_2=- 6

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^2-2x-48=0
Substitute

x= 8

8^2-2( 8)-48? =0
â–¼
Simplify
CalcPow

Calculate power

64-2(8)-48? =0
Multiply

Multiply

64-16-48? =0
SubTerms

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=- 6.

x^2-2x-48=0
Substitute

x= - 6

( - 6)^2-2( - 6)-48? =0
â–¼
Simplify
CalcPow

Calculate power

36-2(- 6)-48? =0
MultNegNegOnePar

- a(- b)=a* b

36+12-48? =0
AddSubTerms

Add and subtract terms

0=0 ✓

Again we created a true statement. x=- 6 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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Multiplying a Polynomial by a Monomial 19 (Page 81)
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arrow_right 7 Solving ax^2+bx+c=0 p.83
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