1. 2
ax bx c

2. Factorization with Algebra Tiles
 Pg. 565

3. 2
Factoring ax bx c
1. Factor out the GCF (if it exists) & rewrite the
trinomial so that the leading coefficient is positive.
2. Find the product of a and c. Let’s call it ac.
3. Create a T-table.
4. Write all integer factors of ac in the 1st column.
5. Write the sum of those factors in the 2nd column.
6. Identify the pair of factors whose sum is b.
7. Use the BOX method.

4. Factor the box way
y = ax2 + bx + c Factor 1st Factor 2nd
Column Column
Factor
1st ax2 (1st Factor)x
Row
Factor
2nd (2nd factor)x c
Row
(Factor 1st Column + Factor 2nd Column)(Factor 1st Row + Factor 2nd Row)

5. Examples
Factor.
1. 2x2 7 x 3
2
2. 3n 14n 5
3. 4x 2
12x 7

6. Example 4 Write and solve a polynomial equation
DISCUS
An athlete throws a discus from an initial height of 6
feet and with an initial vertical velocity of 46 feet per
second.
a. Write an equation that gives the height (in feet) of
the discus as a function of the time (in seconds)
since it left the athlete’s hand.
b. After how many seconds does the discus hit the
ground?

7. Example 4 Write and solve a polynomial equation
SOLUTION
a. Use the vertical motion model to write an equation
for the height h (in feet) of the discus. In this case,
v = 46 and s = 6 .
h = –16t2 + vt + s Vertical motion model
h = –16t2 + 46t + 6 Substitute 46 for v and 6 for s.
b. To find the number of seconds that pass before the
discus lands, find the value of t for which the height
of the discus is 0. Substitute 0 for h and solve the
equation for t.

8. Example 4 Write and solve a polynomial equation
0 = –16t2 + 46t + 6 Substitute 0 for h.
0 = –2(8t2 – 23t – 3 ) Factor out – 2.
0 = –2(8t + 1 ) ( t – 3 ) Factor the trinomial. Find
factors of 8 and – 3 that
produce a middle term
with a coefficient of – 23.
8t + 1 = 0 or t – 3 = 0 Zero-product property
1
t =– or t = 3 Solve for t.
8

9. Example 4 Write and solve a polynomial equation
1
The solutions of the equation are – and 3. A negative
8
solution does not make sense in this situation, so
1
disregard – .
8
ANSWER The discus hits the ground after 3 seconds.

10. Example 5 Multiple Choice Practice
The height of a triangle is 6 inches less than 4 times the
base. The area of the triangle is 54 square inches. What
is the base of the triangle?
4 in. 4.5 in. 6 in. 54 in.
1
Use the area formula A = bh with h = 4b – 6 and A = 54.
2
1
b ( 4b – 6 ) = 54 Write an equation to model area.
2
2b2 – 3b – 54 = 0 Simplify and subtract 54 from each side.
( 2b + 9 ) ( b – 6 ) = 0 Factor left side.

11. Example 5 Multiple Choice Practice
2b + 9 = 0 or b – 6 =0 Zero-product property
9
b =– or b =6 Solve for b.
2
Disregard the negative value of b.
ANSWER The correct answer is C.

12. 9.7 Warm-Up (Day 1)
Factor.
1. 3t 2 8t 4
2
2. 4s 9s 5

13. 9.7 Warm-Up (Day 2)
Factor.
1. 2h 2 13h 7
2. 2 y2 5y 3

14. 9.7 Warm-Up (Day 3)
Factor.
2
1. 5m 6m 1
2. 3x 2 x 2