Page 124 - Math Course 2 (Book 1)

Trinomials: ax + bx + c
2

2
2
Factor 3x + 7x – 5. 0 = –4(4t – 16t + 7) Factor out –4.
There are no factors whose sum is 7. Therefore, 0 = 4t – 16t + 7 Divide each side by –4.
2
2
3x + 7x – 5 cannot be factored using integers.
2
0 = (2t – 7)(2t – 1) Factor 4t – 16t + 7.
2
3x + 7x – 5
Answer
is a prime polynomial. 2t – 7 = 0 or 2t – 1 = 0 Zero Product Property
2t = 7 2t = 1 Solve each equation.

Solve Equations by Factoring t = t = 1
7
2 2
Example The solution are and seconds. The f rst time
1
7
2
2
represents how long it takes the rocket to reach a
2
2
Solve 18b – 19b – 8 = 3b – 5b.
height of 30 feet on its way up. The second time
2
2
18b – 19b – 8 = 3b – 5b. Original equation represents how long it take for the rocket to reach
the height of 30 feet again on its way down. Thus
2
15b – 14b – 8 = 0 Rewrite so one
side. the rocket will be in f ight for 3.5 seconds before
landing.
(5b + 2)(3b – 4) = 0 Factor the left side.
5b + 2 = 0 or 3b – 4 = 0 Zero Product Answer 3.5 seconds
Property.

5b = –2 3b – 4 = 0 Solve each
equation.
2 4 Your Turn!
–
b = b =
5 3
Determine Whether a Polynomial is Prime
{ 2 4 { Factor 3x – 5x + 3.
2
–
Answer The solution set is ,
5
3
A. (3x + 1)(x – 3)
B. prime
C. (3x – 1)(x – 3)
Real World Example D. (3x – 3)(x – 1)
ROCKETS Answer
Ms. Nguyen’s science class built an air-
launched model rocket for a competition.
When they launched their rocket outside
the classroom, the rocket landed in a
nearby tree. If the launch pad was 2 feet above the
ground, the initial velocity of the rocket was 64 feet
per second, and the rocket landed 30 feet above the
ground, how long was the rocket in f ight? Use the
2
equation h = –16t + vt + s.

2
h = –16t + vt + s Vertical motion model
2
30 = –16t + 64t + 2 h = 30, v = 64, s = 2
2
0 = –16t + 64t – 28 Subtract 30 from each side

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