Warm Up #10 Multiply the polynomial. 1. (x + 2)(x + 3)(x + 1)

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Warm Up #10 Multiply the polynomial. 1. (x + 2)(x + 3)(x + 1) ANSWER (x2 + 5x + 6)(x + 1) 2. (2x – 1)(2x + 1) ANSWER 4x2 – 1 3. (x – 7)2 ANSWER x2 – 14x + 49

Check HW 5.3

Find a common monomial factor EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x3 + 2x2 – 15x = x(x2 + 2x – 15) Factor common monomial. = x(x + 5)(x – 3) Factor trinomial. b. 2y5 – 18y3 = 2y3(y2 – 9) Factor common monomial. = 2y3(y + 3)(y – 3) Difference of two squares c. 4z4 – 16z3 + 16z2 = 4z2(z2 – 4z + 4) Factor common monomial. = 4z2(z – 2)2 Perfect square trinomial

Sum and Difference of Cubes:

Write each monomial as a cube and apply either of the rules. Rewrite as cubes Apply the rule for sum of cubes:

Rewrite as cubes Apply the rule for difference of cubes:

GUIDED PRACTICE for Examples 1 and 2 Factor the polynomial completely. 2. 3y5 – 75y3 1. x3 – 7x2 + 10x

2b2(2b + 7)(4b2 –14b + 49) GUIDED PRACTICE for Examples 1 and 2 Factor the polynomial completely. 3. 16b5 + 686b2 2b2(2b + 7)(4b2 –14b + 49)

(w – 3)(w2 + 3w + 9) GUIDED PRACTICE for Examples 1 and 2 Factor the polynomial completely. 4. w3 – 27 (w – 3)(w2 + 3w + 9)

Factor by Grouping EXAMPLE 3 Factor the polynomial x3 – 3x2 – 16x + 48 completely. x3 – 3x2 – 16x + 48 = x2(x – 3) – 16(x – 3) Factor by grouping. = (x2 – 16)(x – 3) Distributive property = (x + 4)(x – 4)(x – 3) Difference of two squares

Factor polynomials in quadratic form EXAMPLE 4 Factor polynomials in quadratic form Factor completely: (a) 16x4 – 81 and (b) 2p8 + 10p5 + 12p2. a. 16x4 – 81 = (4x2)2 – 92 Write as difference of two squares. = (4x2 + 9)(4x2 – 9) Difference of two squares = (4x2 + 9)(2x + 3)(2x – 3) Difference of two squares Factor common monomial. b. 2p8 + 10p5 + 12p2 = 2p2(p6 + 5p3 + 6) Factor trinomial in quadratic form. = 2p2(p3 + 3)(p3 + 2)

GUIDED PRACTICE for Examples 3 and 4 Factor the polynomial completely. 5. x3 + 7x2 – 9x – 63 ANSWER (x + 3)(x – 3)(x + 7)

GUIDED PRACTICE for Examples 3 and 4 Factor the polynomial completely. 6. 16g4 – 625 (4g2 + 25)(2g + 5)(2g – 5) ANSWER

GUIDED PRACTICE for Examples 3 and 4 Factor the polynomial completely. 7. 4t6 – 20t4 + 24t2 4t2(t2 – 3)(t2 – 2 ) ANSWER

Class/Homework Assignment Workbook 5.4 (multiples of 3)