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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
10. Roots and Zeros
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Exercise 2 Page 77

How can factoring out the GCF help you apply the Zero Product Property?

Roots: x=0, x=-8, x=-4
Number and Type of Roots: three real roots

Practice makes perfect

To solve the given equation, we will start by factoring out the GCF. Next, we will apply the Zero Product Property to solve the equation.

x^3+12x^2+32x=0
FactorOut

Factor out x

x(x^2+12x+32 ) =0
ZeroProdProp

Use the Zero Product Property

lcx=0 & (I) x^2+12x+32=0 & (II)

From Equation (I), we found that one root is x=0. To find other roots, we will solve Equation (II). Note that this is a quadratic equation. We will solve it by factoring.

x^2+12x+32=0
Rewrite

Rewrite 12x as 8x+4x

x^2+8x+4x+32 = 0
FactorOut

Factor out x

x(x+8)+4x+32 = 0
FactorOut

Factor out 4

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

Factor out (x+8)

(x+8)(x+4) = 0

Now, let's use the Zero Product Property for the second time to solve the quadratic equation.

(x+8)(x+4) = 0
ZeroProdProp

Use the Zero Product Property

lcx+8=0 & (I) x+4=0 & (II)
SubEqn

(I): LHS-8=RHS-8

lx=-8 x+4=0
SubEqn

(II): LHS-4=RHS-4

lx=-8 x=-4

These roots of the quadratic equation are also roots of the given equation. Roots x=0, x=- 8, x=- 4 We see that there are three roots. All three of them are real.

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arrow_right Exercises p.77-79
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