1. 5.5 Solving Polynomial Equations
Part 1

2. Factoring Patterns

3. 1 8 27 64
125
216
343
512
729
1000
Perfect Cubes

4. A. Factor the polynomial x 3 – 729
A. Factor the polynomial x 3 – 729. If the polynomial cannot be factored, write prime.

5. What’s the first thing we do when we factor?
Pull out the GCF!
Examples: Factor the expression.
1. 64h4 – 27h
2. x3 y + 343y
What’s the first thing we do when we factor?

6. B. Factor the polynomial
24x 5 + 3x 2y 3. If the polynomial cannot be factored, write prime.

8. A. Factor the polynomial
a 2 + 3ay + 2ay 2 + 6y 3. If the polynomial cannot be factored, write prime.

9. B. Factor the polynomial
x 3 + 5x 2 – 4x – 20. If the polynomial cannot be factored, write prime.

10. You try! 1. Factor the polynomial
d 3 + 2d 2 + 4d + 8. If the polynomial cannot be factored, write prime.
You try!

11. 2. Factor the polynomial 64x 9 + 27y 5
2. Factor the polynomial 64x y 5. If the polynomial cannot be factored, write prime.
You try!

12. You try! 3. Factor the polynomial
r 3 + 4r2 – 9r – 36. If the polynomial cannot be factored, write prime.
You try!

13. You try! 4. Factor the polynomial
54x x 2y 3. If the polynomial cannot be factored, write prime.
You try!

14. Solving Polynomial Equations
Algebra 2
5.5 Day 2
Solving Polynomial Equations

15. Quadratic Form

16. Quadratic Form
It is like factoring a quadratic – just not second degree.
Examples:
x4 + 10x x4 – 6x2 – 27

17. Quadratic Form
Examples: 3. 25x4 – x6 – 20x4 + 24x2

18. Solve polynomials by factoring
Put the polynomials in standard form
Factor as far as you can – starting with the GCF – be careful
Set all the factors with variables equal to zero
Solve these new equations
Solve polynomials by factoring

19. Examples: Solve.
x2 + 2x = 0

20. Examples: Solve.
2. 54x3 – 2 = 0

21. 3. 3x3 + 7x2 = 12x 4. x3– 18 = - 2x2 + 9x
Solve.

22. 5. x 4 – 29x = 0
Solve.