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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 51 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.

4, 2

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start factoring the expression!

x^2-6x+8=0
WriteDiff

Write as a difference

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

Factor out x

x(x-2)-4x+8=0
FactorOut

Factor out - 4

x(x-2)-4(x-2)=0
FactorOut

Factor out (x-2)

(x-4)(x-2)=0

Solving

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

(x-4)(x-2)=0
ZeroProdProp

Use the Zero Product Property

lcx-4=0 & (I) x-2=0 & (II)
AddEqn

(I): LHS+4=RHS+4

lx=4 x-2=0
AddEqn

(II): LHS+2=RHS+2

lx_1=4 x_2=2

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=4.

x^2-6x+8=0
Substitute

x= 4

4^2-6( 4)+8? =0
â–¼
Simplify
CalcPow

Calculate power

16-6(4)+8? =0
MultNegPos

(- a)b = - ab

16-24+8? =0
AddSubTerms

Add and subtract terms

0=0 ✓

Substituting and simplifying created a true statement, so we know that x=4 is a solution of the equation. Let's move on to x=2.

x^2-6x+8=0
Substitute

x= 2

2^2-6( 2)+8? =0
â–¼
Simplify
CalcPow

Calculate power

4-6(2)+8? =0
MultNegPos

(- a)b = - ab

4-12+8? =0
SubTerms

Subtract terms

0=0 ✓

Again, we created a true statement. x=2 is indeed a solution of the equation.

Subchapter links expand_more
arrow_right 1 Adding and Subtracting Polynomials p.81
11
Adding and Subtracting Polynomials 12 (Page 81)
Adding and Subtracting Polynomials 13 (Page 81)
Adding and Subtracting Polynomials 14 (Page 81)
Adding and Subtracting Polynomials 15 (Page 81)
Adding and Subtracting Polynomials 16 (Page 81)
Adding and Subtracting Polynomials 17 (Page 81)
Adding and Subtracting Polynomials 18 (Page 81)
arrow_right 2 Multiplying a Polynomial by a Monomial p.81
Multiplying a Polynomial by a Monomial 19 (Page 81)
Multiplying a Polynomial by a Monomial 20 (Page 81)
Multiplying a Polynomial by a Monomial 21 (Page 81)
Multiplying a Polynomial by a Monomial 22 (Page 81)
arrow_right 3 Multiplying Polynomials p.81
Multiplying Polynomials 23 (Page 81)
Multiplying Polynomials 24 (Page 81)
Multiplying Polynomials 25 (Page 81)
Multiplying Polynomials 26 (Page 81)
Multiplying Polynomials 27 (Page 81)
arrow_right 4 Special Products p.82
Special Products 28 (Page 82)
Special Products 29 (Page 82)
Special Products 30 (Page 82)
Special Products 31 (Page 82)
Special Products 32 (Page 82)
Special Products 33 (Page 82)
Special Products 34 (Page 82)
arrow_right 5 Using the Distributive Property p.82
Using the Distributive Property 35 (Page 82)
Using the Distributive Property 36 (Page 82)
Using the Distributive Property 37 (Page 82)
Using the Distributive Property 38 (Page 82)
Using the Distributive Property 39 (Page 82)
Using the Distributive Property 40 (Page 82)
Using the Distributive Property 41 (Page 82)
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Using the Distributive Property 43 (Page 82)
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arrow_right 6 Solving x^2+bx+c=0 p.83
Solving x^2+bx+c=0 46 (Page 83)
Solving x^2+bx+c=0 47 (Page 83)
Solving x^2+bx+c=0 48 (Page 83)
Solving x^2+bx+c=0 49 (Page 83)
Solving x^2+bx+c=0 50 (Page 83)
Solving x^2+bx+c=0 51 (Page 83)
Solving x^2+bx+c=0 52 (Page 83)
Solving x^2+bx+c=0 53 (Page 83)
Solving x^2+bx+c=0 54 (Page 83)
Solving x^2+bx+c=0 55 (Page 83)
arrow_right 7 Solving ax^2+bx+c=0 p.83
Solving ax^2+bx+c=0 56 (Page 83)
Solving ax^2+bx+c=0 57 (Page 83)
Solving ax^2+bx+c=0 58 (Page 83)
Solving ax^2+bx+c=0 59 (Page 83)
Solving ax^2+bx+c=0 60 (Page 83)
Solving ax^2+bx+c=0 61 (Page 83)
Solving ax^2+bx+c=0 62 (Page 83)
Solving ax^2+bx+c=0 63 (Page 83)
Solving ax^2+bx+c=0 64 (Page 83)
arrow_right 8 Differences of Squares p.84
Differences of Squares 65 (Page 84)
Differences of Squares 66 (Page 84)
Differences of Squares 67 (Page 84)
Differences of Squares 68 (Page 84)
Differences of Squares 69 (Page 84)
Differences of Squares 70 (Page 84)
Differences of Squares 71 (Page 84)
Differences of Squares 72 (Page 84)
Differences of Squares 73 (Page 84)
arrow_right 9 Perfect Squares p.84
Perfect Squares 74 (Page 84)
Perfect Squares 75 (Page 84)
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Perfect Squares 79 (Page 84)
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arrow_right 10 Roots and Zeros p.85
Roots and Zeros 85 (Page 85)
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Roots and Zeros 87 (Page 85)
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Roots and Zeros 89 (Page 85)