5.5 Solving Polynomial Equations Part 1

Factoring Patterns

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

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

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?

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

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

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

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

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

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

You try! 4. Factor the polynomial 54x 5 + 128x 2y 3. If the polynomial cannot be factored, write prime. You try!

Solving Polynomial Equations Algebra 2 5.5 Day 2 Solving Polynomial Equations

Quadratic Form  

Quadratic Form It is like factoring a quadratic – just not second degree. Examples: x4 + 10x2 + 16 2. x4 – 6x2 – 27

Quadratic Form Examples: 3. 25x4 – 36 4. 4x6 – 20x4 + 24x2

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

Examples: Solve. x2 + 2x = 0

Examples: Solve. 2. 54x3 – 2 = 0

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

5. x 4 – 29x 2 + 100 = 0 Solve.