Warm-Up Exercises Factor out a common binomial EXAMPLE 1 2x(x + 4) – 3(x + 4) a. 3y 2 (y – 2) + 5(2 – y) b. Factor – 1 from ( 2 – y ). Distributive property.

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Factor out a common binomial EXAMPLE 1 2x(x + 4) – 3(x + 4) a. SOLUTION 3y 2 (y – 2) + 5(2 – y) b. 2x(x + 4) – 3(x + 4) = (x + 4)(2x – 3) a. The binomials.

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Warm-Up Exercises Factor out a common binomial EXAMPLE 1 2x(x + 4) – 3(x + 4) a. 3y 2 (y – 2) + 5(2 – y) b. Factor – 1 from ( 2 – y ). Distributive property Factor the expression.

Warm-Up Exercises Factor by grouping EXAMPLE 2 x 3 + 3x 2 + 5x a y 2 + y + yx + x b. SOLUTION = x 2 (x + 3) + 5(x + 3) = (x + 3)(x 2 + 5) x 3 + 3x 2 + 5x + 15 = (x 3 + 3x 2 ) + (5x + 15) a. y 2 + y + yx + x = (y 2 + y) + (yx + x) b. = y(y + 1) + x(y + 1) = (y + 1)(y + x) Group terms. Factor each group. Distributive property Group terms. Factor each group. Distributive property Factor the polynomial.

Warm-Up Exercises Factor by grouping EXAMPLE 3 Factor 6 + 2x. x3x3 – 3x23x2 – SOLUTION x 3 – 3x 2 + 2x – 6 x 3 – 6 + 2x – 3x 2 = Rearrange terms. (x 3 – 3x 2 ) + (2x – 6) = Group terms. x 2 (x – 3 ) + 2(x – 3) = Factor each group. (x – 3)(x 2 + 2) = Distributive property

Warm-Up Exercises GUIDED PRACTICE for Examples 1, 2 and 3 Factor the expression. 1. x(x – 2) + (x – 2) 2. a 3 + 3a 2 + a y 2 + 2x + yx + 2y

Warm-Up Exercises Factor completely EXAMPLE 4 Factor the polynomial completely. a.a. n 2 + 2n – 1 SOLUTON

Warm-Up Exercises Factor completely EXAMPLE 4 Factor the polynomial completely. b.b. 4x 3 – 44x x SOLUTION b.b. 4x 3 – 44x x Factor out 4x.

Warm-Up Exercises Factor completely EXAMPLE 4 Factor the polynomial completely. c.c. 50h 4 – 2h 2 SOLUTION c.c. 50h 4 – 2h 2

Warm-Up Exercises GUIDED PRACTICE for Example 4 Factor the polynomial completely. 4. 3x 3 – 12x 5. 2y 3 – 12y y 6. m 3 – 2m 2 + 8m

Warm-Up Exercises Solve a polynomial equation EXAMPLE 5 Factor out 3x. Solve 3x x 2 = – 24x. 3x x 2 = – 24x Write original equation. Add 24x to each side. Factor trinomial. Zero-product property Solve for x.

Warm-Up Exercises GUIDED PRACTICE for Example 5 Solve the equation. 7. w 3 – 8w w = 0 8. x 3 –25x 2 = 0 9. c 3 – 7c c = 0