# Factoring trinomials ax2

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```					Factoring trinomials
ax² + bx +c
a=1
x² + bx +c
Product is C

Sum is B
Factor the trinomials
Example: x² + 7x + 12
a = 1 b = 7 c = 12

We need factors of 12 (2 #’s that multiply to 12) that add
up to 7

Factors of 12: 12 and 1    2 and 6 3 and 4

We must always check our answer by foil, box method, or
distributing!!!!! We must ALWAYS SHOW THE CHECK!
Example:

x² + 9x +20

a = 1 b = 9 c = 20

Factors of 20: 20 and 1; 2 and 10; 4 and 5

Example: x² -8x +15

A = 1 b = -8 c = 15

Factors of 15: 5 and 3; 15 and 1

None of those add up to -8

Factors of 15: -5 and -3; -15 and -1

Example: x² + 4x – 12
A = 1 b = 4 c = -12
Factors of -12: 12 and -1; -12 and 1; 2 and -6; 6 and -2;
3 and -4; 4 and -3

Example: x² - 3x – 40

A = 1 b = -3 c = -40

Factors of -40: 1 and -40; 40 and -1; 2 and -20; 20 and -
2; 4 and -10; 10 and -4; 5 and -8; 8 and -5

Let’s look for a hint!
x² + 9x +20 = (x+4)(x+5)       ax² + bx +c = ( + )( + )

x² -8x +15 = (x-5)(x-3)        ax² - bx +c = ( - ) ( - )

x² + 4x – 12 = (x + 6)(x-2)    ax² + bx - c = ( + )( - )

x² - 3x – 40 = (x – 8)(x +5)   ax² - bx – c = ( + )( - )
Practice
1. x² + 9x +18        1. (x + 6)(x + 3)

2. x² -13x + 22       2. (x – 11)(x-2)

3. x² + 5x – 36       3. (x + 9)( x – 4)

4. x² - x – 42        4. (x – 7)(x + 6)

5. X² + 4x - 10
X² + 4x - 10
• When we are unable to find the two factors to
add up to the middle term we are unable to
factor our polynomial!

• We call these polynomials prime!

• A prime polynomial is not factorable!
What happens when there are two
variables?
Example: x² + 5xy + 6y²

Answer: (x + #y)(x + #y)

Factors of 6y² that add up to 5y!
1y and 6y or 2y and 3y

Answer: (x + 3y)(x + 2y)
Practice
1. a² - 13ab + 30b²       1. (a -3b)(a – 10b)

2. x² - 4xy – 77y²        2. (x -11y)(x + 7y)
When A does not equal 1
Example: 3m² - 24m – 60

Always check for a GCF!

GCF: 3

3(m² - 8m – 20)

Factor the quotient!
3(m-10)(m + 2)
Practice
1. x³ + 3x² - 4x           1. X (x² + 3x – 4)
this is not ax² + bx +c      X(x +4)(x – 1)

2. 7x² + 14xy – 21y²       2. 7(x² + 2y – 3y²)
7(x + 3y)(x – 1y)
3. 2t⁵ - 14t⁴ + 24t³
3. 2t³(t² - 7t + 12)
2t³(t – 4)(t – 3)

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