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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Solving Quadratic Equations by Factoring

Finish the assignment

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Exercise 80 Page 176

Begin by factoring 3x^2 out.

0, 3, -3, 2, and -2

Practice makes perfect

We will begin by factoring 3x^2 out. Let's do it!

3x^6-39x^4+108x^2=0

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Factorize

Factor out 3x^2

3x^2(x^4-13x^2+36)=0

Rewrite -13^2 as -4x^2-9x^2

3x^2(x^4-4x^2-9x^2+36)=0

Factor out x^2

3x^2(x^2(x^2-4)-9x^2+36)=0

Factor out -9

3x^2(x^2(x^2-4)-9(x^2-4))=0

Factor out (x^2-4)

3x^2(x^2-9)(x^2-4)=0

ExpandDiffSquares

(a+b)(a-b)=a^2-b^2

3x^2(x-3)(x+3)(x-2)(x+2)=0

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Solve using the Zero Product Property

Use the Zero Product Property

3x^2=0 x-3=0 x+3=0 x-2=0 x+2=0

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

x^2=0 x-3=0 x+3=0 x-2=0 x+2=0

(I): sqrt(LHS)=sqrt(RHS)

x=0 x-3=0 x+3=0 x-2=0 x+2=0

(II): LHS+3=RHS+3

x=0 x=3 x+3=0 x-2=0 x+2=0

(III): LHS-3=RHS-3

x=0 x=3 x=-3 x-2=0 x+2=0

(IV): LHS+2=RHS+2

x=0 x=3 x=-3 x=2 x+2=0

(V): LHS-2=RHS-2

x=0 x=3 x=-3 x=2 x=-2

The solutions to the equation are 0, 3, -3, 2, and -2.

Subchapter links

Exercises p.174-177