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Mr. Borosky Section 5.5 Algebra 2 5.5 Apply the Remainder and Factor Theorem p. 362-368 Objective: 1. You will use theorems to divide and factor polynomials. Polynomial Long Division – a method used to divide polynomials similar to the way you divide numbers. Go over parts of a Division problem. Quotient is the answer of a division Dividend is what is being divided Divisor is what you are dividing by Division Algorithm – is one of the following Dividend = Quotient + Remainder Divisor Divisor Or Dividend = Quotient * Divisor + Remainder Go Over example on Long Division of 873 ÷ 14 Notice that the Division Process ends when the remainder is ZERO or is of lower degree than the divisor. Synthetic Division – an efficient way to Divide a Polynomial by a Binomial of the form x – c. A method that uses only Coefficients to display the process of Dividing a Polynomial in “x” by x – c. Go Over Example 2x3 – 10x2 + 9x + 15 divided by x – 3. here c = 3. 1. Write down the Coefficients of the Dividend 2. Write the “c” value outside of the coefficients of the dividend 3. Bring down the First coefficient 4. Multiply c by the first coefficient to get the number under the 2nd coefficient 5. Add the top and 2nd row 6. Repeat step 4 until you get to the end 3 | 2 -10 9 15 ____________6_____-12_________-9____ | 2 -4 -3 | 6 So that is 2x2 – 4x – 3 + 6 / (x – 3) Remainder Theorem – if a polynomial f(x) is divided by x – k, then the remainder “r” = f(k) Factor Theorem – a polynomial f(x) has a factor “x – k” if and only if f(k) = 0. 5.5 Apply the Remainder and Factor Theorem p. 362-368 Page 1 of 1