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Bellwork 1. Find the product. Write in standard form. 2x(x+2)(x-3) 2. Factor completely: 4x³ -24x²+32x 3. Factor completely: 4. Factor completely: 5. Factor completely: 8x³ +12x² -8x 6. Divide by HAND: 12,356÷3 Lesson7 .3 Products and Factors of Polynomials DAY 2 Objectives: Day 1 Multiply polynomials. Factor polynomials. Day 2 Use substitution to determine factors of a function. Divide by using long division. Day 3 Divide by using synthetic division. Find the zeros of the function: 1.) What are the zeros of the function? 2.) Now, write the factors of the function! Practice #2: 1.) Find the zeros 2.) Write the factors of the function Practice #2: Find the zeros, write the factors, and then write the equation of the function. The Factor Theorem states the relationship between the linear factors of a polynomial expression and the zeros of the related polynomial. FACTOR Ex THEOREM x-r is a factor of the polynomial expression that defines the function P if and only if r is a solution of P(x) =0, that is if and only if P(r)=0. EXAMPLE: Use substitution to determine whether x+2 is a factor of : x³ - 2x² - 5x + 6. Practice: Use substitution to determine whether the given linear expression is a factor of the polynomial. #1)x² +x +1; x-1 Answer NO #2) x³ + 3x²-18x-40; x-4 Answer YES #3) x² + 2x +1; x+2 Answer NO DIVIDING POLYNOMIALS Example 1: x³+ 3x² -4x -12 divided by x-2 Example 2: x³+ 3x² +3x +2 divided by x² +x +1 DIVIDING POLYNOMIALS *remainders* Example 1: 8x³+ 12x² +6x +5 divided by 2x+1 Example 2: 6x² + 2x -5 divided by 3x + 5 Lesson7.3 Page 446 (62-78 EVENS)