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Section 9-5 Factoring Trinomials
SPI 23G: select one of the factors of a quadratic equation
Objective:
• Factor Trinomials
• Prime factors: numbers that are only divisible by 1 and
itself
• Coefficient: constant in front of a variable
• Multiply Binomials: (x + 3)(x + 5) = x2 + 8x + 15
• Quadratic equation: the highest exponent is 2; (i.e. x2)
Factoring a Quadratic Equation
x2 + bx + c (b and c are constants) into Two Binomials
Factor x2 + 8x + 15.
(x + 3)(x + 5)
How do you get the first term (x2)? x ∙ x
How do you get the second term (8x)? 5x + 3x
How do you get the third term (15)? 3 ∙ 5
Find the factors of 15. Identify the pair that has a sum of 8.
Factors of 15
1 and 15
3 and 5
Sum of Factors
16
8
x2 + 8x + 15 = (x + 3)(x + 5).
Factoring a Quadratic Equation
Factor g2 + 7g + 10
Both conditions must be true
Factors of 10
Sum of Factors
1 ∙ 10
11
2∙5
7
Factors of the problem are (g + 2)(g + 5)
How does the factors change when you have a negative
2d term?
Factor g2 - 7g + 10
Both conditions must be true
Factors of 10
Sum of Factors
-1 ∙ -10
-11
-2 ∙ -5
-7
Factors of the problem are (g - 2)(g - 5)
Factoring a Quadratic Equation
How does the factors change when the last term is negative?
a. Factor x2 + 13x – 48.
Identify the pair of factors of –48 that
has a sum of 13.
x2 + 13x – 48 = (x + 16)(x – 3)
Factors of –48 Sum of Factors
1 and –48
–47
48 and –1
47
2 and –24
–22
24 and –2
22
3 and –16
–13
16 and –3
13
What happens when the 2d and 3d terms are negative?
b. Factor n2 – 5n – 24.
Identify the pair of factors of –24 that
has a sum of –5.
n2 – 5n – 24 = (n + 3)(n – 8)
Factors of –24
1 and –24
24 and –1
2 and –12
12 and –2
3 and –8
Sum of Factors
–23
23
–10
10
–5
What happens when there are 2 variables?
Factor
d2
+ 17dg –
60g2.
Identify the pair that has a
sum of 17.
d2 + 17dg – 60g2 =
(d – 3g)(d + 20g)
Factor h2 – 4hk – 77k2.
h2 – 4hk – 77k2 =
(h + 7k)(h – 11k)
Find the factors of –60.
Factors of –60 Sum of Factors
1 and –60
–59
60 and –1
59
2 and –30
–28
30 and –2
28
3 and –20
–17
20 and –3
17
Factors of –77 Sum of Factors
1 and –77
–76
77 and –1
76
11 and –7
4
7 and –11
-4