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

2. EXAMPLE 2 Factor the sum or difference of two cubes Factor the polynomial completely. a. x 3 + 64 = (x + 4)(x 2 – 4x + 16) Sum of two cubes b. 16z 5 – 250z 2 Factor common monomial. = 2z 2 (2z) 3 – 5 3 Difference of two cubes = 2z 2 (2z – 5)(4z 2 + 10z + 25) = x 3 + 4 3 = 2z 2 (8z 3 – 125)

3. GUIDED PRACTICE for Examples 1 and 2 Factor the polynomial completely. 1. x 3 – 7x 2 + 10x SOLUTION x 3 – 7x 2 + 10x= x 3 – 7x 2 + 10x = x( x 2 – 7x + 10) = x( x – 5 )( x – 2 ) Factor common monomial. Factor trinomial.

4. GUIDED PRACTICE for Examples 1 and 2 2. 3y 5 – 75y 3 SOLUTION 3y 5 – 75y 3 = 3y 3 (y 2 – 25) = 3y 3 (y – 5)( y + 5 ) Factor common monomial. Difference of two squares

5. GUIDED PRACTICE for Examples 1 and 2 3. 16b 5 + 686b 2 SOLUTION 16b 5 + 686b 2 = 2b 2 (8b 3 + 343) = 2b 2 (2b + 7)(4b 2 –14b + 49 ) Factor common monomial. Difference of two cubes

6. GUIDED PRACTICE for Examples 1 and 2 4. w 3 – 27 SOLUTION w 3 – 27 = w 3 – (3) 3 = (w – 3)(w 2 + 3w + 9) Difference of two cubes