2. In Arithmetic (3)(5) = 15 Factors Product multiply We multiply factors to form a product. Factor We Factor a number by expressing it as a product of factors. 15 = (3)(5) number Factors The operations of multiplying and factoring are inverses; that is, each operation reverses the other.

3. In Algebra 4(x + 2)=4x +8 Factors Product expand We expand an expression to form a product. Factor We Factor a polynomial by expressing it as a product of factors. 4x + 8=4(x + 2) polynomial Factors The operations of multiplying and factoring are inverses; that is, each operation reverses the other.

4. EXAMPLES Factor fully, 2x 3 + 4x 2 Step 1: Factor each term of the polynomial 2x 3 = 2 * x * x * x 4x 2 = 2 * 2 * x * x We identify the common factors in green. GCF is 2x 2 Therefore the GCF is 2x 2 Step 2: Remove the GCF from each term. Step 3: We write each term as a product of the GCF and another monomial 2x 3 = 2x 2 (x) 4x 2 = 2x 2 (2) 2x 3 + 4x 2 = 2x 2 (x) + 2x 2 (2) Step 4: We use the Distributive Law to write the sum as a product. 2x 2 (x + 2) 2x 3 + 4x = 2x 2 (x + 2)

5. Example Factor Fully: -6y + 3y 2 – 3y 3 6y = 2 * 3 * y 3y 2 = 3 * y * y 3y 3 = 3 * y * y * y GCF = 3y -6y + 3y 2 – 3y 3 = 3y(-2) + 3y(y) + 3y(-y 2) = 3y(-2 + y – y 2 ) Step 1 Step 2 & 3 Step 3

6. Example Simplify, then factor: 5x 2 – 3x + 2 – x 2 + 11x + 10 Step 1: Simplify 5x 2 – x 2 – 3x + 11x + 2 + 10 4x 2 + 8x + 12 Collect like terms Simplify 4x 2 = 2 * 2 * x * x 8x = 2 * 2 * 2 * x 12 = 2 * 2 * 3 GCF = 4 4x 2 + 8x + 12 = 4(x 2 ) + 4(2x) + 4(3) = 4(x 2 + 2x + 3)

7. Class work Check Homework from Lesson 26 in share folder Page 346 - #3-5,8,9 Page 347 - #12,14,15