1. Ch 11.5 Dividing Polynomials
Objective:
To divide polynomials using long division.

2. Definitions Rules dividend ÷ divisor = quotient
Multiply the first term of the divisor by a value that will eliminate the first term of the dividend
Distribute that value to the divisor and subtract it from the dividend
3) Repeat 1 & 2 until there is a remainder

3. a x Example 1 Example 2 -4 +3 − ( ) a2 − 7a − ( ) x2 + 5x -4a + 36 3x
(a2 – 11a + 36) ÷ (a – 7)
(x2 + 8x + 18) ÷ (x + 5) a -4 x +3
− ( )
a2 − 7a
− ( )
x2 + 5x
-4a
+ 36 3x
+ 18
− ( )
-4a + 28
− ( )
3x + 15 8 3
a – x
a - 7
x + 5

4. v 5n Example 3 Example 4 -7 +7 − ( ) v2 + 8v − ( ) 5n2 − 30n -7v − 57
(v2 + v − 57) ÷ (v + 8)
(5n2 − 23n − 33) ÷ (n − 6) v -7 5n +7
− ( )
v2 + 8v
− ( )
5n2 − 30n
-7v
− 57 7n
− 33
− ( )
-7v − 56
− ( )
7n − 42 -1 9
v – 5n
v + 8
n − 6

5. 1) 2) 3) 4) r + 8 + 5 n – 8 + 8 r + 7 n + 5 x + 9 + -3 m + 10 + -9
Classwork 1) 2)
(r2 + 15r + 61) ÷ (r + 7)
(n2 – 3n – 32) ÷ (n + 5) r
n –
r + 7
n + 5 3) 4)
(m2 + 12m + 11) ÷ (m + 2)
(x2 – x – 93) ÷ (x – 10) x m
x − 10
m + 2

6. 5) 6) 7) 8) x + 3 + 3 n + 8 + -3 x + 5 n + 3 x + 4 + -3 8m – 9 + -3
(x2 + 8x + 18) ÷ (x + 5)
(n2 + 11n + 21) ÷ (n + 3) x n
x + 5
n + 3 7) 8)
(x2 + x – 15) ÷ (x – 3)
(8m2 + 39m – 57) ÷ (m + 6) x
8m –
x − 3
m + 6