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Warm Up #10. Multiply the polynomial. 1. ( x + 2)( x + 3)( x + 1). (x 2 + 5 x + 6)( x + 1). ANSWER. 2. (2 x – 1)(2 x + 1). 4 x 2 – 1. ANSWER. 3. ( x – 7) 2. x 2 – 14 x + 49. ANSWER. Check HW 5.3. EXAMPLE 1. Find a common monomial factor.

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## Multiply the polynomial.

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**Warm Up #10**Multiply the polynomial. 1. (x + 2)(x + 3)(x + 1) (x2 + 5x + 6)(x + 1) ANSWER 2. (2x– 1)(2x + 1) 4x2– 1 ANSWER 3. (x – 7)2 x2 – 14x + 49 ANSWER**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. = 2y3(y2 – 9) b. 2y5 – 18y3 Factor common monomial. = 2y3(y + 3)(y – 3) Difference of two squares = 4z2(z2 – 4z + 4) c. 4z4 – 16z3 + 16z2 Factor common monomial. = 4z2(z – 2)2 Perfect square trinomial**Apply the rule for sum of cubes:**Write each monomial as a cube and apply either of the rules. Rewrite as cubes**Apply the rule for difference of cubes:**Rewrite as cubes**for Examples 1 and 2**GUIDED PRACTICE Factor the polynomial completely. 2. 3y5 – 75y3 1.x3 – 7x2 + 10x**for Examples 1 and 2**GUIDED PRACTICE Factor the polynomial completely. 3. 16b5 + 686b2 2b2(2b + 7)(4b2 –14b + 49)**for Examples 1 and 2**GUIDED PRACTICE 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. = x2(x – 3) –16(x – 3) x3– 3x2– 16x + 48 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 completely:(a) 16x4 – 81and(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)**for Examples 3 and 4**GUIDED PRACTICE Factor the polynomial completely. 5. x3 + 7x2 – 9x – 63 ANSWER (x+ 3)(x – 3)(x + 7)**for Examples 3 and 4**GUIDED PRACTICE Factor the polynomial completely. 6. 16g4 – 625 (4g2 + 25)(2g + 5)(2g – 5) ANSWER**for Examples 3 and 4**GUIDED PRACTICE Factor the polynomial completely. 7. 4t6 – 20t4 + 24t2 4t2(t2 – 3)(t2 – 2 ) ANSWER

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