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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
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