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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. Using the Distributive Property
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Exercise 11 Page 39

Use the Zero Product Property.

0, 3/4

Practice makes perfect

To solve the given equation, let's factor and solve using the Zero Product Property. At the end, we will check that our answer is correct.

Factoring

Since it appears that the expression has a GCF, let's factor that out. After that, we will proceed to factoring.

20p^2-15p
FactorOut

Factor out 5p

5p(4p-3)=0

Solving

Now we can apply the Zero Product Property to solve.

5p(4p-3)=0
ZeroProdProp

Use the Zero Product Property

lc5p = 0 & (I) 4p-3=0 & (II)
DivEqn

(I): .LHS /5.=.RHS /5.

lcp = 0 & (I) 4p-3=0 & (II)
AddEqn

(II): LHS+3=RHS+3

lcp = 0 & (I) 4p=3 & (II)
DivEqn

(II): .LHS /4.=.RHS /4.

lcp = 0 & (I) p= 34 & (II)

We found that the solutions of the equation are 0 and 34.

Checking

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

20p^2-15p=0
Substitute

p= 0

20( 0)^2-15( 0)? =0
CalcPow

Calculate power

20(0)-15(0)? =0
ZeroPropMult

Zero Property of Multiplication

0-0? =0
SubTerm

Subtract term

0=0 ✓

Since substituting and solving resulted in a true statement, we know that p=0 is a solution of the equation. Let's now check p= 34.

20p^2-15p=0
Substitute

p= 3/4

20( 3/4)^2-15( 3/4)? =0
CalcPow

Calculate power

20*9/16-15*3/4? =0
MoveLeftFacToNum

a*b/c= a* b/c

20*9/16-15*3/4? =0
Multiply

Multiply

180/16-45/4? =0
ReduceFrac

a/b=.a /4./.b /4.

45/4-45/4? =0
SubFrac

Subtract fractions

0=0 ✓

This is also a true statement, so we know that p= 34 is a solution of the equation.

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Exercises 2 (Page 39)
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