1. 5.4 – Factoring ax2 + bx + c

2. When you have x2 + bx + c, to factor it, we found the factors of the constant that added to the middle term
But, when you have ax2 + bx + c, things become a little more tricky
We will still use a similar method

3. Factoring ax2 + bx + c
We will have to take into account the leading coefficient a, when a is not 1
Example. Factor 2x2 + 3x - 5
New Method:
1) Multiply a and c together

4. 2) Find the factors of a(c) that add to the middle term
Factors that add to 3?

5. 3) “Split” the middle term as each factor
Split 3 as…

6. 4) Group together the first two, and last two terms
Find any common factors they share

7. 5) Pull out the “common binomial”
Should always be the same binomial

8. 6) Write the second binomial as the common factors

9. Rule of Thumb
When you factor these, you will always have a common binomial, and a second binomial made up of the common factors
If you do not get back to the common binomial, double check your signs or the GCF you pulled out

10. Example. Factor 5x2 + 8x + 3

11. Example. Factor 5x2 + 13x + 6

12. Example. Factor 3x2 + 9x + 6

13. Example. Factor 5z2 + 25z - 70

14. Assignment
Pg. 244
3-9, odd