2.5Solve Equations in Factored FormVocabulary Let a and b be real numbers. If ab = 0, then = 0 or =...

2.5 Solve Equations in Factored FormVocabularyVocabulary

Let a and b be real numbers. If ab = 0, then = 0 or = 0.

Zero-Product Property a b

2.5 Solve Equations in Factored Form

Example 1 Use the zero-product propertyUse the zero-product property

Solve 045 xxWrite original equation. Write original equation. 045 xx

______________ ______________ property. property.

Zero-product0_____ 0_____or

Solve for Solve for xx. . x = ______ or x = _____

5x 4x5 4

The solutions of the equation are ______________.5 and 4Check. Substitute each solution into the original equation to check.

04__5__?

5 5 04__5__?

4 40_____

90 0__ 0 0_____?

09 0__ 0

2.5 Solve Equations in Factored FormCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises.

036 .1 xx

06 x 03 x6x

058 .2 xx

08 x 05 x8x

Binomial Trinomial 4 or more terms

Methods of Factoring

GCF GCF GCFDifference of

SquaresPerfect Square

TrinomialTwo Binomials

(Shortcut)Two Binomials

(cross)

Grouping

Example 2 Solve an equation by factoringSolve an equation by factoring

Solve 0153 2 xxWrite original equation. Write original equation. 0153 2 xxFactor left side. (GCF) Factor left side. (GCF) 0_________ 3x x 5Zero-product property. Zero-product property. 0___ 0_____or

Solve for Solve for xx. . x = ______ or x = _____

x3 5x0 5

The solutions of the equation are ______________.0 and 5

Example 3 Solve an equation by factoringSolve an equation by factoring

Solve bb 249 2 Write original equation. Write original equation. bb 249 2 Subtract _____ from Subtract _____ from each side. each side.

24b0249 2 bb

Factor left side. (GCF) Factor left side. (GCF) 0_________ 3b b3 8Zero-product property. Zero-product property. 0___ 0_____or

Solve for Solve for bb. . x = ______ or x = _____

b3 83 b0 3

The solutions of the equation are ______________.0 and

2.5 Solve Equations in Factored FormExample 3 Solve a multi-step problemSolve a multi-step problemFountain:Fountain: A fountain sprays water from the ground into the air with an initial velocity of 20 feet per second. After how many seconds does it land on the ground?

SolutionStep 1 Write a model for the water’s height above ground.

svtth 216 Vertical motion model. Vertical motion model.

____16 2 tth vv = ___ and = ___ and ss = ___. = ___. 20 200 0Simplify. Simplify. ____16 2 th t20

2.5 Solve Equations in Factored FormExample 3 Solve a multi-step problemSolve a multi-step problemFountain:Fountain: A fountain sprays water from the ground into the air with an initial velocity of 20 feet per second. After how many seconds does it land on the ground?

SolutionStep 2 Substitute __ for h. When the water lands, its height above the ground is __ feet. Solve for t.

____16__ 2 t Substitute __ for Substitute __ for hh..

______________ Factor right side. Factor right side. 00 0t20

4t t4 5Zero-product property. Zero-product property. 0___ 0_______or Solve for Solve for xx. . t = ______ or t = _____

t4 54 t0 25.1

The water lands on the ground ______ after it is sprayed.1.25

07 Solve .3 2 dd

0 d d 70d 07 d

bb 28 Solve .4 2

0 2 b b4 102 b 014 b

028 2 bb

4 4b 0

5. In Example 4, suppose the initial velocity is 18 feet per second. After how many seconds does the water land on the ground? svtth 216

2160 t t18 0 2 t t8 9

02 t 098 t9t8

8 8t 0t 125.1

The water lands on the ground ______ after it is sprayed.1.125

2.5Solve Equations in Factored FormVocabulary Let a and b be real numbers. If ab = 0, then = 0 or =...

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