Factoring Worksheet With Examples Page 27
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50A model for the vertical motion of a projected object is given by the equation
2
h = -16 t
+ vt + s, where h is the height in feet, t is the time in seconds, v is
the initial upward velocity in feet per second, and s is the initial height of the
object in feet.
PEP RALLY
At a pep rally, small foam
Height of
reception
footballs are launched by cheerleaders using
a sling-shot. How long is a football in the air
if a student catches it on its way down 26 feet
Factoring When
above the gym floor?
Height of
a Is Negative
release
2
When factoring a
h = -16 t
+ vt + s
Vertical motion model
26 ft
trinomial of the form
2
2
26 = -16 t
+ 42t + 6
h = 26, v = 42, s = 6
a x
+ bx + c where a
6 ft
is negative, it is helpful
2
0 = -16 t
+ 42t - 20
Subtract 26 from
to factor out a negative
each side.
monomial.
0
t
2
42 ft/s
v
0 = -2(8 t
- 21t + 10)
Factor out -2.
2
0 = 8 t
- 21t + 10
Divide each side by -2.
2
0 = (8t - 5)(t - 2)
Factor 8 t
- 21t + 10.
8t - 5 = 0 or t - 2 = 0
Zero Product Property
8t = 5
t = 2
Solve each equation.
_
5
t =
8
_
5
The solutions are
second and 2 seconds.
8
The first time represents how long it takes the football to reach a height of
26 feet on its way up. The later time represents how long it takes the ball to
reach a height of 26 feet again on its way down. Thus, the football will be in
the air for 2 seconds before the student catches it.
4
.
Six times the square of a number plus 11 times the number equals 2.
What are possible values of x?
Personal Tutor at
Examples 1–2
Factor each trinomial, if possible. If the trinomial cannot be factored
(pp. 442–443)
using integers, write prime.
2
2
2
1. 3 a
+ 8a + 4
2. 2 t
- 11t + 7
3. 2 p
+ 14p + 24
2
2
2
4. 2 x
+ 13x + 20
5. 6 x
+ 15x - 9
6. 4 n
- 4n - 35
Example 3
Solve each equation. Check the solutions.
(p. 443)
2
2
2
7. 3 x
8. 10 p
9. 6 n
+ 11x + 6 = 0
- 19p + 7 = 0
+ 7n = 20
10.
CLIFF DIVING
Example 4
Suppose a diver leaps from the edge of a cliff 80 feet above
(p. 444)
the ocean with an initial upward velocity of 8 feet per second. How long
will it take the diver to enter the water below?
444
444
Chapter 8 Factoring
Chapter 8 Factoring
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