1. Divide a polynomial by a binomial
EXAMPLE 2
Divide a polynomial by a binomial
Divide x2 + 2x – 3 by x – 1.
SOLUTION
STEP 1
Divide the first term of x2 + 2x – 3 by the first term of x – 1. x
x – 1
x2 + 2x – 3
Think: x x = ?
x2 – x
Multiply x and x – 1. 3x
Subtract x2 – x from x2 + 2x.

2. Divide a polynomial by a binomial
EXAMPLE 2
Divide a polynomial by a binomial
STEP 2
Bring down –3. Then divide the first term of 3x – 3 by the first term of x – 1.
x – 1
x2 + 2x – 3
x2 – x
3x – 3 x
+ 3
Think: 3x x = ?
3x – 3
Multiply 3 and x – 1.
Subtract 3x – 3 from 3x – 3.
ANSWER
(x2 + 2x – 3) (x – 1) = x + 3

3. Divide a polynomial by a binomial
EXAMPLE 3
Divide a polynomial by a binomial
Divide 2x2 + 11x – 9 by 2x – 3. x
2x2 –3x
14x – 21
+ 7
2x – 3
2x2 + 11x – 9
Multiply x and 2x – 3.
14x – 9
Subtract 2x2 – 3x. Bring down – 9.
Multiply 7 and 2x – 3. 12
Subtract 14x – 21.
ANSWER
(2x x – 9) (2x – 3) = x + 7 + 12
2x – 3

4. GUIDED PRACTICE
for Examples 2 and 3
Divide: (a2 + 3a – 4) (a + 1)
a + 2 +
ANSWER
– 6
a + 1
Divide: (9b2 + 6b + 8) (3b – 4)
ANSWER
3b + 6 + 32
3b – 4