1. Questions about 2.8 HW…

2. 2.9 Factor Polynomials Completely 2.6-2.9 Test: Friday Midterm: March 11

3. Vocabulary Factoring a common monomial from pairs of terms, then looking for a common binomial factor is called factor by grouping. A factorable polynomial with integer coefficients is factored completely if it is written as a product of un-factorable polynomials with integer coefficients.

4. Example 1: Factor the expression: 5x 2 (x – 2) – 3(x – 2) Solution: Since (x – 2) appears twice =(x – 2)(5x 2 – 3) Factor the expression: 7y(5 – y) + 3( y – 5) Solution: Factor a -1 from (5 – y) to make it (y – 5) -7y(y – 5) + 3( y – 5) =(-7y + 3)(y – 5)

5. You Try: Factor 11x(x – 8) + 3(x – 8) Factor 5x(y – 4) + 2(4 – y)

6. Example 2: Factor by grouping: m 3 + 7m 2 – 2m – 14 Solution Group terms: (m 3 + 7m 2 ) + (-2m – 14) Factor each group: m 2 (m + 7) - 2(m + 7) =(m + 7)(m 2 – 2)

7. You Try: Factor the polynomial: n 3 + 30 + 6n 2 + 5n

8. Example 3: Factor the polynomial completely:  5x 3 – 55x + 90x Solution Factor out the GCF: 5x(x 2 – 11x + 18) Factor what’s in the parenthesis: 5x(x – 2)(x – 9)

9. You Try: Factor Completely  4x 3 – 36x  2y 3 – 16y 2 + 32y

10. Example 4: Solve the equation: 7x 3 + 14x 2 = 105x Solution Move 105x: 7x 3 + 14x 2 – 105x = 0 Factor out the GCF: 7x(x 2 + 2x – 15) = 0 Factor the trinomial: 7x(x + 5)(x – 3) = 0 Set each factor equal to zero: 7x = 0 x + 5 = 0 x – 3 = 0 Solve for x: x = 0, x = -5, x = 3

11. You Try: Solve the equation: 2c 3 + 8c 2 = 42c

12. Homework: P. 95 #1 – 29 odd