1. 12/23/20159-4 9-4 Division and The Remainder Theorem

2. 12/23/20159-4 Long Division: DivisorDividend Remainder (rx)

3. 12/23/20159-4 Polynomial Division Dividend(polynomial): p(x)Divisor: d(x) Quotient: q(x)

4. 12/23/20159-4 Polynomial Division To divide Two Polynomials: Fill in terms for any missing exponentFill in terms for any missing exponent Divide the leading term of the “dividend” by the leading term of the “divisor”Divide the leading term of the “dividend” by the leading term of the “divisor” Multiply the answer you get by the entire divisor and subtract from divdendMultiply the answer you get by the entire divisor and subtract from divdend Divide the leading term of this answer by the leading term of the divisorDivide the leading term of this answer by the leading term of the divisor Repeat until there is nothing left to divide.Repeat until there is nothing left to divide.

5. 12/23/20159-4 Polynomial Division

6. 12/23/20159-4 Polynomial Division

7. Remainders and Polynomial Division: If after the polynomial division, r(x) = 0, what does that mean? If r(x) ≠ 0, what must be true of the degree of r(x) and why? p(x) = q(x)·d(x) + r(x) 12/23/20159-4

8. 12/23/20159-4 Remainder Theorem If a polynomial f(x) is divided by x – c, then the remainder is equal to f(c) (the value of the function when x = c): Let’s look at the last example:

9. Try one: Divide by. Then check using the remainder theorem. 12/23/20159-4 Remainder (rx) NOTE: This theorem only applies if the divisor is LINEAR!!!!

10. Last Practice: Divide by. 12/23/20159-4