1. WARM UP Multiply each Polynomial. 1. (x + 3)(x + 2) 2. (x + 7)(x – 7) 3.5(x + 3) 4. (x + 7)(x – 4) We are simplifying by using the _______________ property.

2. Unit 1: Rational Expressions Lesson 1a: Factoring and Simplifying NC Goal 1.03: Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems

3. Performance Standards TLW… 1.Find the Greatest Common Factor (GCF) of a polynomial. 2.Factor out a monomial from a polynomial. 3.Factor polynomials. Essential Questions 1.How do you find the GCF of a polynomial? 2.How do you factor out a monomial from a polynomial? 3.How do you factor a polynomial with a coefficient = 1? 4.How do you factor a polynomial with a coefficient ≠ 1?

4. 1. How do you find the GCF of a polynomial? 12x + 16 G.C.F. ______ 15X 3 – 20X 2 G.C.F. _____

5. 2. How do you factor out a monomial from a polynomial? 4X 3 – 12X 2 + 16x 1. Find the G.C.F. _______ ____( ) 2. Put the G.C.F. on the outside of the parenthesis 3. Divide coefficients from original polynomial by the G.C.F. and subtract exponents

6. 3. How do you factor a polynomial with a coefficient = 1? x 2 - 13x + 30 1. Put the last term on top 2. Put the middle term on the bottom 3. Find two numbers you can multiply to get the top number but add to get the bottom number 4. Write your two factors *If can’t be factored then it is prime

7. 4. How do you factor a polynomial with a coefficient ≠ 1? 2X 2 + 11X +12 1. Multiply the coefficient of the first term and the last term _____ 2. Remove the leading coefficient ____ and rewrite the polynomial using the new last term _____ 3. Factor 4. 5.

8. You Try 1.-8X 4 + 24X 7 G.C.F. ___ 2. 10x 5 – 70X + 90 G.C.F. ___ Factor. 3. -2X 2 – 10X + 14 4. 3x 2 y – 21xy 5. a 2 + 4a+ 3 6. x 2 - 3x - 18 7. 3c 2 + 8c - 3 8. 2s 2 – 13s - 24

9. Work Time Answers 1.(x + 2) (x + 3)2. (y + 1)(y + 4)3. (m + 5)(m + 7) 4. (p + 3)(p + 5)5. (a + 2)(a + 6)6. (n + 2)(n + 2) 7. (x + 3) ( x + 6)8. prime9. (y – 2)(y - 4) 10. (c – 3)(c – 5)11. (m – 1)(m – 1)12. (b – 4)(b – 5) 19. (7b – 2)(b – 2)20. (3y + 5)(y – 2)21. (2c + 1)(3c + 4) 22. (2x – 1)(5x + 2) 23. (4m -1)(3m – 2) 1.4(x + 4) 2. 3y(y + 4) 3. 5x(2 + xy)4. prime 5.5r(3 + 4s) 6. 7a(2b + 3) 7. 3xy(3 – y)8. 6mn(2m – 3n) 9. 2ab(4 + ab) 10. 4ab(4ac – 9b) 11. prime 12. 2xy(4xy 2 -5)

10. Closure Pre-Test Connections: #s 1, 2, 3

11. Homework Factor each of the Polynomials 1.x 2 + 4x + 32. x 2 – 4x – 21 3. x 2 + 8x – 94. 2x 2 + 5x + 3 5. 3x 2 + 2x – 86. 3x 2 – 6x – 24