1. 5.4 – Factor and Solve Polynomial Functions

2. 5.4 – Factor and Solve Polynomial Functions

3. 5.4 – Factor and Solve Polynomial Functions
Example 1:
Factor the polynomial completely.
x3 + 2x2 – 15x
2y5 – 18y3
4z4 – 16z3 + 16z2

4. 5.4 – Factor and Solve Polynomial Functions

5. 5.4 – Factor and Solve Polynomial Functions
Example 2:
Factor the polynomial completely.
a. x3 + 64
b. 16z5 – 250z2

6. 5.4 – Factor and Solve Polynomial Functions
For some polynomials, you can factor by grouping pairs of terms that have a common monomial factor. The pattern for factoring by grouping is shown below:
ra + rb + sa + sb = r(a+b) + s(a+b)=
(r + s)(a + b)

7. 5.4 – Factor and Solve Polynomial Functions
Example 3:
Factor the polynomial x3 – 3x2 – 16x + 48

8. 5.4 – Factor and Solve Polynomial Functions
Example 4:
Factor completely:
16x4 – 81
2p8 + 10p5 + 12p2

9. 5.4 – Factor and Solve Polynomial Functions
Example 5:
What are the real number solutions of the equation 3x5 + 15x = 18x3?