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Unformatted text preview: Objectives
Factor the sum and difference of cubes (and use this factoring to solve polynomial functions) polynomial Factor polynomials that are “quadratic in form” Solve Polynomial equations using a graphing calculator graphing Section 6.4
Solving polynomial Solving equations equations Warm up
Factor! Factor! Sum and Difference of Cubes
Write this down! Memorize it! Write 4 x − 25 2 4 x + 16 x 2 a 3 + b 3 = (a + b)(a 2 − ab + b 2 ) a 3 − b 3 = (a − b)(a 2 + ab + b 2 ) x3 − 8 x 4 − 9 x 2 − 18 What are “perfect cubes”? Just factor!
x −8
3 Now let’s solve!
3
Predict how many solutions we’ll have… 27 x + 8 27 x 3 + 1 = 0 1 You Try!
x3 + 8 = 0 One more type of factoring
There are two ways to think about this one… Just Factor it! x 4 − 9 x 2 − 18 Use substitution to make the problem easier Now let’s Solve x 4 − x 2 = 12 Summary: Look at all the factoring Summary: we can do! we
0 = 2x3 − x2 − x 0 = x3 + 1 0 = 25 x 2 − 16 0 = x 4 + 7 x 2 + 10 What do we do when we can’t factor? factor? 3 2 x + 3x = x + 3 x 3 − 2 x 2 = −3
We can graph these just like we did quadratics! quadratics! Homework #________
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 Fall '09
 Johnson
 Algebra, Factoring, Polynomials, Equations

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