Factoring Trinomials

1
Factoring Trinomials

• Factoring Flow Chart, parts 1, 2 and 3

No
Difference of Squares? 2 terms/-/( )2
GCF?
No
Yes
Yes
Factor (a b)(a b)
Factor The box
Factor GCF(leftovers)
2
Factoring The Box

• Recall (x 8)(3x 1)

3x
1
x
3x2
1x
3x2 25x 8
8
24x
8
Multiply the diagonals of the box. What happens?
3
Factoring The Box
(x 2)(4x 3)

• Factor 4x2 11x 6

4x
3
leftovers
Key step GCF of row is this
x
4x2
x
3

We need 2 numbers that multiply to 24x2 and add
up to 11x, so both terms must have an x (like
terms).
2
x
6
8

There are no negatives in the problem, so both
numbers must be positive.
Sum 11x
Product (4x2)(6)24x2
(1)(24) (2)(12) (3)(8) (4)(6)
4
Factoring The Box
(x 5)(2x 1)

• Factor 2x2 11x 5

x
5
leftovers
Key step GCF of row is this
2x
2x2
x
10

We need 2 numbers that multiply to 10x2 and add
up to 11x, so both terms must have an x (like
terms).
1
x
5
1

There are no negatives in the problem, so both
numbers must be positive.
Sum 11x
Product (2x2)(5)10x2
(1)(10) (2)(5)
5
Factoring The Box
(8x 3)(x 2)

• Factor 8x2 19x 6

x
2
leftovers
Key step GCF of row is this
8x
8x2
x
16

We need 2 numbers that multiply to 48x2 and add
up to 19x, so both terms must have an x (like
terms).
3
x
6
3

There are no negatives in the problem, so both
numbers must be positive.
Sum 19x
Product (8x2)(6)48x2
6
Factoring The Box

• Factor 7x2 12x 5

7x2
x

We need 2 numbers that multiply to 35x2 and add
up to 12x, so both terms must have an x (like
terms).
x
5

There are no negatives in the problem, so both
numbers must be positive.
Sum 12x
Product (7x2)(5)35x2
7
Factoring The Box

• Factor x2 15x 56

x2
x

We need 2 numbers that multiply to 56x2 and add
up to 15x, so both terms must have an x (like
terms).
x
56

There are no negatives in the problem, so both
numbers must be positive.
Sum 15x
Product (x2)(56)56x2