3.4 Lesson: Factoring Quadratics when a is not 1

(x - 5)(x + 6)

1) Look at your trinomial for this one. What is our "a" value?

2) Think about the steps during foil. Is there an affect on our "b" value?

3) Think about if you had to factor this, notice the b value is the addition of the end two terms and c is the product of them.

(3x + 2)(x - 6)

1) Think about what's different here, what changes are in our FOIL pattern?

2) How does this affect our b value in our trinomial?
3) Is our c value affected at all?

1) Our b has at least one part multiplied by a factor of "a" before they are added.

2) c remains unchanged
3) To find "b" we may have to change our method slightly

When a is not 1

1) Our b value is just the sum of our last two terms in each binomial.

2) c is just the product of them
3) So "products of c that add to b works as a way of finding the factor!

When a is 1

3x² + 5x - 2 = 0

1) First I want you to find the factors of "a"

2) Then I want you to create some binomial brackets. Leave space between x and your parenthesis for a number!
(_x__)(_x__)
(_x__)(_x__)

Doesn't quite roll of the tongue as well.

Factors of c times factors of a that add to b

(3x__)(1x__)



(-3x__)(-1x__)

Factors of a get set up in binomails

2x² - x - 3 = 0

1) Make factors of "a" into binomials
2) Factor c
3) Factors of c time factors of a that add to b
4) Solve your binomials

5x² + 28x - 12 = 0

When you're done do your homework!