Assignment: Use the Zero Product Property
Choose any three (3) of the following four problems to solve. Be sure to show all your work.
1. A child launches a toy rocket from the top of a slide at the park. Suppose the equation
16t 2 28t 8 0 can be used to find how many seconds it will take for the rocket to hit
the ground.
a. Write the equation in factored form.
4(t - 2)(4t + 1)
b. Use the zero product property to solve the equation. Show all the steps needed
to find both answers.
c.
4(t - 2) = 0
4(t - 2)/4 = 0/4
t-2=0
t-2+2=0+2
Explain
t = 2 how the solution relates to this situation.
4(2 - 2)(4 * 2 + 1)
4(0)(9)
=0
2. A manufacturing company manufactures a cardboard box with a square base and a
4t + 1 = 0
2
height of4t
15+ inches.
1/4 = 0/4Suppose the equation x 60 x 7,200 0 can be used to find the
length and
t +width
1 = 0 of the base of the box, each measuring x inches.
t+1-1=0-1
t = -1 the equation in factored form.
a. Write
(-120 + -1x)(60 + -1x)
4(-1 - 2)(4 * (-1) +1)
4(-3)(-3)
= 36
b. Use the zero product property to solve the equation. Show all the steps needed
to find both answers.
c.
-120 + -1x = 0
-120 + -1x + 120 = 0 + 120
-1x = 120
-1x/-1 = 120/-1
Explain
x = -120 how the solution relates to this situation.
(-120 + -1 * -120)(60 + -1 * -120)
(0)(180)
=0
60 + -1x = 0
60 + -1x - 60 = 0 - 60
-1x = -60
-1x/-1 = -60/-1
x = 60
(-120 + -1 * 60)(60 + -1 * 60)
(-180)(0)
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3. City engineers decide to build a rectangular dog park that has an area of 3,600 square
yards, where the length of the park is 10 more yards than twice its width. The equation
x 2 5 x 1,800 0 can be used to find the width of the dog park.
a. Write the equation in factored form.
(-45 + -1x)(40 + -1x)
b. Use the zero product property to solve the equation. Show all the steps needed
to find both answers.
c.
-45 + -1x = 0
-45 + -1x + 45 = 0 + 45
-1x = 45
-1x/-1 = 45/-1
x = -45
Explain how the solution relates to this situation.
(-45 + -1 * -45)(40 + -1 * -45)
(0)(85)
=0
40 + -1x = 0
40 + -1x - 40 = 0 - 40
4. A graphic designer uses a photo editing program to increase both the height and width of
-1x = -40
a square-1x/-1
image
by 3 inches. Suppose the equation x 2 6x 55 0 can be used to find
= -40/-1
the height
x =and
40 width of the original image.
(-45 + the
-1 * equation
40)(40 + -1in*factored
40)
a. Write
form.
(-85)(0)
(-11
=
0 + -1x)(5 + -1x)
b. Use the zero product property to solve the equation. Show all the steps needed
to find both answers.
c.
-11 + -1x = 0
-11 + -1x + 11 = 0 + 11
-1x = 11
-1x/-1 = 11/-1
x = -11 how the solution relates to this situation.
Explain
(-11 + -1 * -11)(5 + -1 * -11)
(0)(16)
=0
5 + -1x = 0
5 + -1x - 5 = 0 - 5
-1x = -5
-1x/-1 = -5/-1
x=5
(-11 + -1 * 5)(5 + -1 * 5)
(-16)(0)
=0
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