1. Warm up Factor the expression.
1. 2x2 + 6x x2 + 2x – x2 – 500

2. Solving Polynomial Equations
5.5
Solving Polynomial Equations

3. Sum and Difference of cubes
(a3 + b3) = (a + b)(a2 – ab + b2)
(a3 – b3) = (a – b)(a2 + ab + b2)

4. Perfect Cubes 1 8 27 64
125
216
343
512
729
1000

5. Example 1: Factor the expression.
a) x3 +125
b) 8y3 – 27

6. What’s the first thing we do when we factor?
Take out the GCF!
Example 2: Factor the expression.
a) 64h4 – 27h
b) x3 y + 343y

7. Factor by Grouping
1. Divide the terms in a polynomial into two groups.
2. Take out a GCF from each group, so the remaining factors are the same.
3. Take out the new GCF.
4. Factor the factors if possible.

8. Example 3 : Factor the expression.
a) 2x3 – 3x2 – 10x + 15

9. Example 3: Factor the expression.
b) x2 y2 – 3x2 – 4y2 + 12

10. Example 3: Factor the expression.
c) bx2 + 2a + 2b + ax2

11. Quadratic Form
Example: x6 + x3 – 2 = (x3)2 + x3 – 2

12. Quadratic Form Example 4: x4 – 6x2 – 27 b) 25x4 – 36
It is like factoring a quadratic – just not second degree.
Example 4:
x4 – 6x2 – 27
b) 25x4 – 36
c) 4x6 – 20x3 + 24

13. Solve polynomials by factoring
Put the polynomials in standard form
Factor as far as you can – starting with the GCF
Set all the factors with variables equal to zero
Solve these new equations
You should have as many solutions as the degree of the polynomial.

14. Example 5: Solve.
x2 + 2x = 0

15. Example 6: Solve.
54x3 – 2 = 0

16. Example 7: Solve.
x 4 – 29x = 0

17. Example 8: Solve.
a) 3x3 + 7x2 = 12x b) x3– 18 = - 2x2 + 9x