Exercise 60 Page 231

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.

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start by writing all the terms on one side of the equals sign. We will also factor out a GCF, if we find one.

6x^2+9x-15=0

▼

.LHS /3.=.RHS /3.

FactorOut

Factor out 3

3(2x^2+3x-5)=0

DivEqn

.LHS /3.=.RHS /3.

2x^2+3x-5=0

WriteSum

Write as a sum

2x^2-2x+5x-5=0

▼

Factor out 2x & 5

FactorOut

Factor out 2x

2x(x-1)+5x-5=0

FactorOut

Factor out 5

2x(x-1)+5(x-1)=0

FactorOut

Factor out (x-1)

(2x+5)(x-1)=0

Solving

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

(2x+5)(x-1)=0

ZeroProdProp

Use the Zero Product Property

lc2x+5=0 & (I) x-1=0 & (II)

SubEqn

(I): LHS-5=RHS-5

l2x=- 5 x-1=0

DivEqn

(I): .LHS /2.=.RHS /2.

lx=- 52 x-1=0

AddEqn

(II): LHS+1=RHS+1

lx_1=- 52 x_2=1

Our answer corresponds to option B.

Subchapter links

Lesson Check p.229

Practice and Problem-Solving Exercises p.229-231

Standardized Test Prep p.231

Mixed Review p.231

Exercise 60 Page 231

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Factoring

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