5.4 – Factoring ax2 + bx + c

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

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

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

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

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

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

6) Write the second binomial as the common factors

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

Example. Factor 5x2 + 8x + 3

Example. Factor 5x2 + 13x + 6

Example. Factor 3x2 + 9x + 6

Example. Factor 5z2 + 25z - 70

Assignment Pg. 244 3-9, 21-37 odd