1. Aim: How do we divide a polynomial by a binomial?
Do Now:

2. Problem 1 Divide each term of the polynomial by the monomial.
Factor each expression.
Divide out the common factors in each expression.
Write in simplified form.

3. Problem 2 Divide each term of the polynomial by the monomial.
Factor each expression.
Divide out the common factors in each expression.
Write in simplified form.

4. Dividing a Polynomial by a Polynomial
The objective is to be able to divide a polynomial by a polynomial by using long division.
Dividend – the number which is being divided.
Divisor – The number that is being divided into the dividend.
Quotient – The result obtained when numbers or expressions are divided.
Remainder – The part that is left over when the divisor no longer goes into the dividend a whole number of times.

6. Division of a Polynomial by a Binomial
Dividend = Divisor x Quotient + Remainder
P(x) = D(x) Q(x) + R(x)
This is called the Division Statement or Division Algorithm.
Divide: x2 + 7x + 2 ÷ (x + 2)
1. The polynomial
must be in descending
order of powers. Any
missing terms are to be
filled with a zero
placeholder.
Multiply x
+ 5
x + 2
x2 + 7x + 2
x2 + 2x
x(x + 2)
= x2 + 2x 5x
+ 2
2. Only the first term is
used when doing the
division.
5x + 10
Divide x2 x -8
= x
3. Multiply your answer
with the entire divisor.
4. Subtract, bring down
the next term and repeat
the process.
P(x) =
(x + 2)
(x + 5)
- 8

7. Division by a Binomial
4x2
- 3x
+ 2
x - 2
4x3 - 11x2 + 8x + 10
4x x2
- 3x2
+ 8x
- 3x2 + 6x 2x
+ 10 2x 14
P(x) = D(x) Q(x) + R(x)
P(x) = (x - 2)(4x2 - 3x + 2) + 14

8. x + 3
X2 divided by x is x. Multiply x-2 by x. x - 2 2 x + x - 15 2 x - 2 x
Subtract 3 x - 15
3x divided by x is 3. Multiply x-2 by 3. 3 x - 6 -
Subtract 9
You Try It

9. 3 x + 2
12x2 divided by 4x is 3x.
Multiply 4x-1 by 3x. 10 4 1 12 5 2 x - + 3 2 12 x -
Subtract - 8 10 x
8x divided by 4x is 2. Multiply 4x-1 by 2. 8 2 x - - 8
Subtract
You Try It

11. Divide: 1. 2.