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

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Presentation transcript:

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

2.5Solve Equations in Factored Form Example 1 Use the zero-product property Solve Write original equation. ______________ property. Zero-product Solve for x. x = ______ or x = _____ The solutions of the equation are ______________. 5 and  4 Check. Substitute each solution into the original equation to check.

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

2.5Solve Equations in Factored Form BinomialTrinomial4 or more terms Methods of Factoring GCF Difference of Squares Perfect Square Trinomial Two Binomials (Shortcut) Two Binomials (cross) Grouping

2.5Solve Equations in Factored Form Example 2 Solve an equation by factoring Solve Write original equation. Factor left side. (GCF) Zero-product property. Solve for x. x = ______ or x = _____ The solutions of the equation are ______________. 0 and  5

2.5Solve Equations in Factored Form Example 3 Solve an equation by factoring Solve Write original equation. Subtract _____ from each side. 24b Factor left side. (GCF) Zero-product property. Solve for b. x = ______ or x = _____ The solutions of the equation are ______________. 0 and 

2.5Solve Equations in Factored Form Example 3 Solve a multi-step problem Fountain: 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? Solution Step 1 Write a model for the water’s height above ground. Vertical motion model. v = ___ and s = ___. Simplify.

2.5Solve Equations in Factored Form Example 3 Solve a multi-step problem Fountain: 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? Solution Step 2 Substitute __ for h. When the water lands, its height above the ground is __ feet. Solve for t. Substitute __ for h. Factor right side. 0 0 Zero-product property. Solve for x. t = ______ or t = _____ The water lands on the ground ______ after it is sprayed. 1.25

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

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

2.5Solve Equations in Factored Form Checkpoint. Complete the following exercises. 5.In Example 4, suppose the initial velocity is 18 feet per second. After how many seconds does the water land on the ground? The water lands on the ground ______ after it is sprayed

2.5Solve Equations in Factored Form