1

5.5 Solving Polynomial EquationsPart 1

2Factoring Patterns

Perfect Cubes

1 8 27 64 125 216 343 512 729 1000

4

• 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

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• B. Factor the polynomial

24x

5 + 3x

2y

3. If the polynomial cannot be factored, write prime.

7

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.

10You try!

• 1. Factor the polynomial d

3 + 2d

2 + 4d + 8. If the polynomial cannot be factored, write prime.

11You try!

• 2. Factor the polynomial 64x

9 + 27y

5. If the polynomial cannot be factored, write prime.

12You try!

• 3. Factor the polynomial r

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

13You try!

• 4. Factor the polynomial 54x

5 + 128x

2y

3. If the polynomial cannot be factored, write prime.

Solving Polynomial Equations

Algebra 2

5.5 Day 2

Quadratic Form

 

Quadratic Form

• It is like factoring a quadratic – just not second degree.

Examples:

1. x4 + 10x2 + 16 2. x4 – 6x2 – 27

Quadratic Form

Examples:

3. 25x4 – 36 4. 4x6 – 20x4 + 24x2

Solve polynomials by factoring

1. Put the polynomials in standard form

2. Factor as far as you can – starting with the GCF – be careful

3. Set all the factors with variables equal to zero

4. Solve these new equations

Examples: Solve.

1. x2 + 2x = 0

Examples: Solve.

2. 54x3 – 2 = 0

Solve.

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

Solve.

5. x 4 – 29x 2 + 100 = 0