Dividing Polynomials

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.

Write the polynomial in ___________ ________.
If any power is missing , use a _______ to hold
the place of that term.
Divide as before.

a simpler process (than long division) for
dividing a polynomial by a binomial

uses ___________ and part of the divisor

1. Write polynomial in ___________ order of the degrees .
2. List the ___________. (If one power is missing, put a
zero to hold that place.)
3. Write the constant _____ of the divisor x - c to the left.
4. Bring down the ___________ coefficient.
5. ___________ the first coefficient by c , write the product
under the 2nd coefficient and add .
6. Multiply this sum by c , write it under the next
coefficient and add. ___________until all coefficients
have been used.
7. 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.

Use Synthetic Division: x³ – 7x – 6 by x + 2.

If the polynomial f(x) is divided by x – c, then
the remainder is the ___________ f(c).

f(x) = (x – c)q(x) + r

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, 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.