5.4 Factor and Solve Polynomial Equations. Find a Common Monomial Factor Monomial: means one term. (ex) x (ex) x 2 (ex) 4x 3 Factor the Polynomial completely.

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Presentation transcript:

5.4 Factor and Solve Polynomial Equations

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 z 2

Sum of Two Cubes a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) 8x = ( + )( - + ) (Ex) x (Ex) 125x 3 + 8

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)

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.

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)

(ex) Factor in Quadratic Form 16g 4 – 25 (ex) 2p p p 2

(ex) 4t 6 – 20t t 2

Find Real Number Solutions (ex) 4x 5 – 40x x (ex) 2x x = 14x 3

HW/CW Page 356 (3,8,10,13,22,24,35)