Download 2.4 Dividing Polynomials

Objective: To divide polynomials
using long and synthetic division,
and to use the remainder and
factor theorems.
Perform long division, as you do with
numbers! Remember, division is repeated
subtraction, so each time you have a new
term, you must ___________ it from the
previous term.
Work from left to right, starting with the
highest degree term.
Just as with numbers, there may be a
remainder left. The divisor may not go into
the dividend evenly.
(x2 + 14x + 45) ÷ (x + 9)
Write the polynomial in ___________ ________.
If any power is missing, use a _______ to hold
the place of that term.
Divide as before.
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a simpler process (than long division) for
dividing a polynomial by a binomial
uses ___________ and part of the divisor
Use Synthetic Division:
1.
2.
3.
4.
5.
6.
7.
Write polynomial in ___________ order of the degrees.
List the ___________. (If one power is missing, put a
zero to hold that place.)
Write the constant _____ of the divisor x - c to the left.
Bring down the ___________ coefficient.
___________ the first coefficient by c, write the product
under the 2nd coefficient and add.
Multiply this sum by c, write it under the next
coefficient and add. ___________ until all coefficients
have been used.
The numbers on the bottom row are the coefficients of
the polynomial ___________. The first power on the
variable will be one _________ than the highest power in
the original polynomial.
If the polynomial f(x) is divided by x – c , then
the remainder is the ___________ f(c).
f(c).
x3 – 7x – 6 by x + 2.
Given f(x) = 3x3 + 4x2 – 5x + 3, use the
remainder theorem to find f(-4).
f(x) = (x – c)q(x) + r
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LONG DIVISION
If a binomial divides into a polynomial with
no remainder, the binomial is a ___________ of
the polynomial.
For the polynomial f(x), if f(c) = 0,
0, then x – c is
a factor of f(x)
Remember . . . If something is a factor, then
it divides the term evenly (with 0 remainder).
Solve the equation 15x3 + 14x2 – 3x – 2 = 0,
given that -1 is a zero of
f(x) = 15x3 + 14x2 – 3x – 2.
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