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5.4 Factor and Solve Polynomial Equations
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Find a Common Monomial Factor Monomial: means one term. (ex) x (ex) x 2 (ex) 4x 3 Factor the Polynomial completely. (1) x 3 + 2x – 15x (2) 2y 5 – 18y 3 (3) 4z 4 – 16z 3 + 16z 2
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Sum of Two Cubes a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) 8x 3 + 27 = ( + )( - + ) (Ex) x 3 + 64 (Ex) 125x 3 + 8
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Difference of Two Cubes a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) (64x 3 – 1) = ( )( ) (Ex) (w 3 – 27) (Ex) (8y 3 – 216)
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Factor By Grouping Factor the Polynomial x 3 – 3x 2 – 16x + 48 Step 1: Place a parenthesis around the the first two terms and another around the second two terms. Step 2: Factor out the GCF in each parenthesis Step 3: Make a new binomial with the two GCF’s taken from the two parenthasis If the binomials are the same, then do not list it twice in the final answer.
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Factor polynomials in quadratic form (ex) 16x 4 – 81 Rewrite by identifying the square roots. (4x 2 ) 2 – (9) 2 Difference of two squares. (4x 2 + 9)(4x 2 – 9) (4x 2 + 9)(2x + 3)(2x – 3)
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(ex) Factor in Quadratic Form 16g 4 – 25 (ex) 2p 8 + 10p 5 + 12p 2
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(ex) 4t 6 – 20t 4 + 24t 2
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Find Real Number Solutions (ex) 4x 5 – 40x 3 + 36x (ex) 2x 5 + 24x = 14x 3
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HW/CW Page 356 (3,8,10,13,22,24,35)
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