1. EXAMPLE 3
Use synthetic division
Divide f (x)= 2x3 + x2 – 8x + 5 by x + 3 using synthetic
division.
SOLUTION
– –
– –21
2 – –16
2x3 + x2 – 8x + 5
x + 3
= 2x2 – 5x + 7 – 16
ANSWER

2. EXAMPLE 4
Factor a polynomial
Factor f (x) = 3x3 – 4x2 – 28x – 16 completely given that
x + 2 is a factor.
SOLUTION
Because x + 2 is a factor of f (x), you know that f (–2) = 0. Use synthetic division to find the other factors.
– –4 – –16 –
3 – –

3. Use the result to write f (x) as a product of two
EXAMPLE 4
Factor a polynomial
Use the result to write f (x) as a product of two
factors and then factor completely.
f (x) = 3x3 – 4x2 – 28x – 16
Write original polynomial.
= (x + 2)(3x2 – 10x – 8)
Write as a product of two
factors.
= (x + 2)(3x + 2)(x – 4)
Factor trinomial.

4. GUIDED PRACTICE
for Examples 3 and 4
Divide using synthetic division.
3. (x3 + 4x2 – x – 1)  (x + 3)
x2 + x – 4 + 11
x + 3
ANSWER
4. (4x3 + x2 – 3x + 7)  (x – 1)
4x2 + 5x + 2 + 9
x – 1
ANSWER

5. GUIDED PRACTICE
for Examples 3 and 4
Factor the polynomial completely given that x – 4 is a factor.
f (x) = x3 – 6x2 + 5x + 12
ANSWER
(x – 4)(x –3)(x + 1)
f (x) = x3 – x2 – 22x + 40
ANSWER
(x – 4)(x –2)(x +5)