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**5.5 Solving Polynomial Equations**

Part 1

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Factoring Patterns

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

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**A. Factor the polynomial x 3 – 729**

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

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**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?

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**B. Factor the polynomial**

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

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**A. Factor the polynomial**

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

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**B. Factor the polynomial**

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

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**You try! 1. Factor the polynomial**

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

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**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!

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**You try! 3. Factor the polynomial**

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

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**You try! 4. Factor the polynomial**

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

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**Solving Polynomial Equations**

Algebra 2 5.5 Day 2 Solving Polynomial Equations

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Quadratic Form

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

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

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**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

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Examples: Solve. x2 + 2x = 0

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Examples: Solve. 2. 54x3 – 2 = 0

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

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5. x 4 – 29x = 0 Solve.

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