1. 4.4 Notes: Factoring Polynomials

4. 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

5. 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)

6. SUM: (a + b)(a2 – ab + b2) DIFFERENCE: (a – b)(a2 + ab + b2)
1) look for GCF
2) make in to perfect cubes to use the formulas above
A) x3 – B) 27x3 – 8 C) 64x3 + 1

7. 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

8. A divisor is a factor of a polynomial is the remainder is zero

10. Finally…..
Show that x + 3 is a factor of f(x) = x4 + 3x3 – x – 3, then factor completely.
Step 1: use synthetic division to determine if x+3 is a factor
Step 2: factor the polynomial.

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