Quiz on Monday on 8-1 to 8-3 and 8-5

Bell Ringer

1. Use the Distributive Property to factor the polynomial 3ab2 + 15a2b2 + 27ab3.

2. 15w – 3v

3. Video on Factoring by Grouping

Factor 4xy + 3y – 20x – 15.

Factor by Grouping with Additive Inverses

Factor 15a – 3ab + 4b – 20.

The solution to an equation is called the root. The root is any value that makes the equation true.

Solve Equations

A. Solve (x – 2)(4x – 1) = 0. Check the solution.

If (x – 2)(4x – 1) = 0, then according to the Zero Product Property, either x – 2 = 0 or 4x – 1 = 0.

(x – 2)(4x – 1) = 0 Original equation

x – 2 = 0 or 4x – 1 = 0 Zero Product Property

x = 2 4x = 1 Solve each equation.

Divide.

Solve Equations

(x – 2)(4x – 1) =0 (x – 2)(4x – 1) = 0

Check Substitute 2 and for x in the original equation.

(2 – 2)(4 ● 2 – 1) = 0? ?

(0)(7) = 0? ?

0 = 0 0 = 0

Solve Equations

B. Solve 4y = 12y2. Check the solution.

Write the equation so that it is of the form ab = 0.

4y = 12y2 Original equation

4y – 12y2 = 0 Subtract 12y2 from each side.

4y(1 – 3y) = 0 Factor the GCF of 4y and 12y2, which is 4y.

4y = 0 or 1 – 3y = 0 Zero Product Property

y = 0 –3y = –1 Solve each equation.Divide.

Solve Equations

Answer: The roots are 0 and . Check by substituting

0 and for y in the original equation.

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A. Solve (s – 3)(3s + 6) = 0. Then check the solution.

B. Solve 5x – 40x2 = 0. Then check the solution.

Use Factoring

FOOTBALL A football is kicked into the air. The height of the football can be modeled by the equation h = –16x2 + 48x, where h is the height reached by the ball after x seconds. Find the values of x when h = 0.

h = –16x2 + 48x Original equation

0 = –16x2 + 48x h = 0

0 = 16x(–x + 3) Factor by using the GCF.

16x = 0 or –x + 3 = 0 Zero Product Property

x = 0 x = 3 Solve each equation.Answer: 0 seconds, 3 seconds

A. 0 or 1.5 seconds

B. 0 or 7 seconds

C. 0 or 2.66 seconds

D. 0 or 1.25 seconds

Juanita is jumping on a trampoline in her back yard. Juanita’s jump can be modeled by the equation h = –14t2 + 21t, where h is the height of the jump in feet at t seconds. Find the values of t when h = 0.