Warm up Factor the expression.

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Presentation transcript:

Warm up Factor the expression. 1. 2x2 + 6x + 4 2. 3x2 + 2x – 1 3. 5x2 – 500

Solving Polynomial Equations 5.5 Solving Polynomial Equations

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

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

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

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

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.

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

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

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

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

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

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.

Example 5: Solve. x2 + 2x = 0

Example 6: Solve. 54x3 – 2 = 0

Example 7: Solve. x 4 – 29x 2 + 100 = 0

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