Factoring Trinomials

Page
2

Again, we will factor trinomials such as

x2 + 7x + 12 back into binomials.

This method does not use tiles, instead we look for the pattern of products and sums!

Factoring Trinomials (Method 2)

If the x2 term has no coefficient (other than 1) .

Step 1: List all pairs of numbers that multiply to equal the constant, 12.

x2 + 7x + 12

12 = 1 • 12

= 2 • 6

= 3 • 4

Slide 10

Factoring Trinomials (Method 2)

Step 2: Choose the pair that adds up to the middle coefficient.

x2 + 7x + 12

12 = 1 • 12

= 2 • 6

= 3 • 4

Step 3: Fill those numbers into the blanks in the binomials:

( x + )( x + )

3

4

x2 + 7x + 12 = ( x + 3)( x + 4)

Slide 11

Factor. x2 + 2x - 24

This time, the constant is negative!

Factoring Trinomials (Method 2)

Step 1: List all pairs of numbers that multiply to equal the constant, -24. (To get -24, one number must be positive and one negative.)

-24 = 1 • -24, -1 • 24

= 2 • -12, -2 • 12

= 3 • -8, -3 • 8

= 4 • -6, - 4 • 6

Step 2: Which pair adds up to 2?

Step 3: Write the binomial factors.

x2 + 2x - 24 = ( x - 4)( x + 6)

Slide 12

Factor. 3x2 + 14x + 8

This time, the x2 term DOES have a coefficient (other than 1)!

Factoring Trinomials (Method 2*)

Step 2: List all pairs of numbers that multiply to equal that product, 24.

24 = 1 • 24

= 2 • 12

= 3 • 8

= 4 • 6

Step 3: Which pair adds up to 14?

Step 1: Multiply 3 • 8 = 24 (the leading coefficient & constant).

Slide 13

( 3x + 2 )( x + 4 )

2

Factor. 3x2 + 14x + 8

Factoring Trinomials (Method 2*)

Step 5: Put the original leading coefficient (3) under both numbers.

( x + )( x + )

Step 6: Reduce the fractions, if possible.

Step 7: Move denominators in front of x.

Step 4: Write temporary factors with the two numbers.

12

4

Slide 14

( 3x + 2 )( x + 4 )

Factor. 3x2 + 14x + 8

Factoring Trinomials (Method 2*)

You should always check the factors by distributing, especially since this process has more than a couple of steps.

= 3x2 + 14 x + 8

= 3x • x + 3x • 4 + 2 • x + 2 • 4

√

3x2 + 14x + 8 = (3x + 2)(x + 4)

Slide 15

Factor 3x2 + 11x + 4

This time, the x2 term DOES have a coefficient (other than 1)!

Factoring Trinomials (Method 2*)

Step 2: List all pairs of numbers that multiply to equal that product, 12.