1. 5.5a – Long Division

2. When using long division, make sure to write the expression in descending order and use a place holder for missing terms.
Ex. What is the missing term?
5x5 + 2x4 - 3x3 – 5x + 1
0x2

3. Divide using long division.
1. (x2 – 2x – 48)  (x + 5) x
x + 5
x2 – 2x – 48
–( ) x2
+ 5x

4. Divide using long division.
1. (x2 – 2x – 48)  (x + 5) x
– 7
13 .
x + 5
x + 5
x2 – 2x – 48
x – 7 –
– – x2
+ 5x
– 7x
– 48
–7x
– 35
– 13

5. Divide using long division.
2. (x3 – x2 + 4x – 10)  (x + 2) x2
– 3x
+ 10
30 .
x + 2
x + 2
x3 – x2 + 4x – 10
x2 – 3x + 10 –
– – x3
+ 2x2
– 3x2
+ 4x
–3x2
– 6x
10x
– 10
10x
+ 20
– 30

6. Divide using long division.
3. (x4 – 7x2 + 9x – 10)  (x – 2) x3
+ 2x2
– 3x
+ 3
x – 2
x4 + 0x3 – 7x2 + 9x – 10 x4
– 2x3
2x3
–7x2
4 .
x – 2
2x3
–4x2
x3 + 2x2 – 3x + 3 –
–3x2
+ 9x
–3x2
+ 6x 3x
– 10 3x
– 6
– 4

7. Divide using long division.
4. (5x4 + 2x3 – 9x + 12)  (x2 – 3x + 4)
16x – 112.
x2 – 3x + 4
5x2 + 17x
5x2
+ 17x
+ 31
x2 – 3x + 4
5x4 + 2x3 + 0x2 – 9x + 12
5x4
–15x3
+20x2
17x3
– 20x2
– 9x
17x3
–51x2
+68x
31x2
–77x
+12
31x2
–93x
+124
16x
–112

8. 5. f(x) = x3 – 3x2 – 16x – 12; x – 6 x2 + 3x + 2 (x – 6)(x2 + 3x + 2)
Given polynomial f(x) and a factor of f(x), factor f(x) completely.
5. f(x) = x3 – 3x2 – 16x – 12; x – 6 x2
+ 3x
+ 2
(x – 6)(x2 + 3x + 2)
x – 6
x3 – 3x2 – 16x – 12 x 2 x3
– 6x2 x 1
3x2
– 16x
2x + x
3x2
–18x 2x
– 12
(x – 6)(x + 2)(x + 1) 2x
– 12

9. Given polynomial f(x) and a factor of f(x), factor f(x) completely.
6. f(x) = x3 – 18x2 + 95x – 126; x – 9 x2
– 9x
+ 14
(x – 9)(x2 – 9x + 14)
x – 9
x3 – 18x2 + 95x – 126 x –7 x3
– 9x2 x –2
– 9x2
+ 95x
–7x +
–2x
– 9x2
+ 81x
14x
– 126
(x – 9)(x – 7)(x – 2)
14x
– 126