2. 4.4 Notes: Factoring Polynomials

3. Factoring using a GCF:
We can start by trying to pull out a GCF. Remember, there WILL be more factoring to do after this!
A) x3 – 4x2 – 5x B) 3y5 – 48y3 C) 5z4 + 30z3 45z2

4. Factoring sum or difference of cubes:
Sum or difference of cubes has:
Only two terms
Two perfect cubes
You need to use one of these two formulas to factor sum or difference of cubes…no other factoring method works!
SUM: (a + b)(a2 – ab + b2) DIFFERENCE: (a – b)(a2 + ab + b2)

5. A) x3 – 125 B) 16s5 + 54s2 C) 64x D) 27x3 - 8

6. Factor by Grouping:
This method is part of the factoring of quadratics method that we have been using.
A) z3 + 5z2 – 4z – 20 B) 3y3 + y2 + 9y + 3 C) x3 + 2x2 – 9x + 18

7. Warm Up:

8. Factoring in “Quadratic” Form
These factor just like quadratics, but have a larger exponent than x2.
A) 16x4 – 81 B) 3p8 + 15p5 + 18p2 C) 2x x9 + 8x5

9. Is it a factor?
To move forward with polynomials, we need to be able to answer the question “Is it a factor?”
What does this mean? It means, is the value or expression something that was used to multiply to make the polynomial given, or is it a “zero” (x – intercept) of the polynomial.
Remember, factors of 24 can be 3 x 8 >>> This means 3 is a factor of 24 because we multiplied it by is a factor of 24 because we multiplied it by 3.
YOUR ANSWER SHOULD BE A ZERO IF IT IS A FACTOR..EVERY TIME!

10. Two ways to determine…..
There are two ways to determine if something is a factor, depending on the information you are given.
EX 1: Is x – 2 a factor of f(x) = x2 + 2x – 4?

11. Another way….
EX 2: Is x + 5 a factor of f(x) = 3x4 + 15x3 – x2 + 25

12. Finally…..
Show that x + 3 is a factor of f(x) = x4 + 3x3 – x – 3, then factor completely.

13. And….
Show that x – 2 is a factor of f(x) = x4 – 2x3 + x – 2 then factor completely.

14. So, any helpful hints for us?
Yes 
If there are two terms…check for difference of squares or sum or difference of cubes.
If there are three terms, check for common factor, then factor like quadratics (first times the last term, those factors that add to the middle)
If there are four terms, factor by grouping (start by splitting the four terms in half).