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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 41 Page 82

Use the Zero Product Property to solve the equation.

0, 2

Practice makes perfect

We want to solve the given equation. At the end we will check that our answer is correct.

Solving

We will begin by solving the equation. x(3x-6)=0To do so, we will use the Zero Product Property.

x(3x-6)=0
ZeroProdProp

Use the Zero Product Property

lcx=0 & (I) 3x-6=0 & (II)
AddEqn

(II): LHS+6=RHS+6

lcx=0 & (I) 3x=6 & (II)
DivEqn

(II): .LHS /3.=.RHS /3.

lcx=0 & (I) x=2 & (II)

We found that the solutions of the equation are 0 and 2.

Checking

To check our answers, we will substitute them for x in the given equation. Let's start with x=0.

x(3x-6)=0
Substitute

x= 0

0(3( 0)-6)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

Since substituting and solving resulted in a true statement, we know that x=0 is a solution of the equation. Let's now check x=2.

x(3x-6)=0
Substitute

k= 2

2(3( 2)-6)? =0
Multiply

Multiply

2(6-6)? =0
SubTerm

Subtract term

2(0)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

This is also a true statement, so we know that x=2 is 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)
Adding and Subtracting Polynomials 14 (Page 81)
Adding and Subtracting Polynomials 15 (Page 81)
Adding and Subtracting Polynomials 16 (Page 81)
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Multiplying a Polynomial by a Monomial 19 (Page 81)
Multiplying a Polynomial by a Monomial 20 (Page 81)
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arrow_right 3 Multiplying Polynomials p.81
Multiplying Polynomials 23 (Page 81)
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arrow_right 4 Special Products p.82
Special Products 28 (Page 82)
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arrow_right 5 Using the Distributive Property p.82
Using the Distributive Property 35 (Page 82)
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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)
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arrow_right 10 Roots and Zeros p.85
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