1. Do Now: Factor the polynomial.
1.) 2x2 – 3x – 20 2.) x2 – 36 3.) x2 + x – 20

2. 4.4: Factoring Polynomials
Algebra II
4.4: Factoring Polynomials

3. Chapter 3 We learned how to factor the following Type Example
General Trinomial
2x2 – 3x – 20 = (2x + 5)(x – 4)
Perfect Square Trinomial
x2 + 8x + 16 = (x + 4)2
Difference of Two Squares
9x2 – 1 = (3x + 1)(3x – 1)
Common Monomial Factor
8x2 + 20x = 4x(2x + 5)

4. Factoring Polynomials
We can also factor polynomials with degree greater than 2. Some can be factored completely using techniques we already know.
A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients.

5. Factoring Polynomials
2(x+1)(x – 4) is factored completely
3x(x2 – 4) is not factored completely because x2 – 4 = (x + 2)(x – 2)

6. Factor: Find Common Monomial
x3 – 4x2 – 5x
3y5 – 48y3
5z4 + 30z3 + 16z2

7. Factoring Cubes
In the second part of the last slide, the special factoring pattern for the difference of two squares was used to factor the expression completely. There are also factoring patterns that we can use to factor cubes.

8. Factoring Cubes Sum of Two Cubes a3 + b3 = (a + b)(a2 – ab + b2)
Difference of Two Cubes
a3 – b3 = (a – b)(a2 + ab + b2)

9. Factor the sum or difference of cubes
1.) x3 – ) 16s5 + 54s2

10. Factoring by grouping.
For some polynomials, you can factor by grouping pairs of terms that have a common monomial factor. This is very similar to our strategy for factoring quadratics of the form ax2 + bx + c when |a| > 1.

11. Factor by grouping
1) z3 + 5z2 – 4z – 20

12. Factoring polynomials in quadratic form
An expression of the form au2 + bu + c, where u is an algebraic expression, is said to be in quadratic form. The factoring techniques we have studied can sometimes be used to factor such expressions.

13. Factor Polynomials in Quadratic Form
16x4 – 81
3p8 + 15p5 + 18p2