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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

Use the Zero Product Property

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

(II): LHS+6=RHS+6

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

(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

x= 0

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

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

k= 2

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

Multiply

2(6-6)? =0

Subtract term

2(0)? =0

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

1 Adding and Subtracting Polynomials p.81

2 Multiplying a Polynomial by a Monomial p.81

3 Multiplying Polynomials p.81

4 Special Products p.82

5 Using the Distributive Property p.82

6 Solving x^2+bx+c=0 p.83

7 Solving ax^2+bx+c=0 p.83

8 Differences of Squares p.84

9 Perfect Squares p.84

10 Roots and Zeros p.85