10.6
Goal
Factoring ax2 bx c
How long will it take a cliff diver to enter the water?
Factor trinomials of the
form ax 2 bx c.
In Example 5 you will use a
vertical motion model to find the
time it takes a cliff diver to enter
the water.
Key Words
• factor a trinomial
• FOIL pattern
• quadratic
To factor a trinomial of the form ax2 bx c, write the trinomial as the product
of two binomials (factored form).
factors of 6
Example:
6x2 22x 20 (3x 5)(2x 4)
b 12 10 22
factors of 20
One way to factor ax2 bx c is to find numbers m and n whose product is a
and numbers p and q whose product is c so that the middle term is the sum of the
Outer and Inner products of FOIL.
mna
ax2 bx c (mx p)(nx q)
b mq np
pqc
EXAMPLE
1
Factor when a and c Are Prime Numbers
Factor 2x2 11x 5.
Write the numbers m and n whose
product is 2 and the numbers
p and q whose product is 5.
m and n
p and q
1, 2
1, 5
Use these numbers to write trial
Trial Factors
Middle Term
factors. Then use the Outer and
Inner products of FOIL to
check the middle term.
(x 1)(2x 5)
(2x 1)(x 5)
5x 2x 7x
10x x 11x
ANSWER 䊳
2x2 11x 5 (2x 1)(x 5).
Factor when a and c Are Prime Numbers
Factor the trinomial.
1. 2x2 7x 3
2. 2x2 5x 3
10.6
3. 3x2 10x 3
Factoring ax2 bx c
603