1. Use synthetic division to divide the polynomial
f(a) = 4a2 – 3a + 6 by a – 2
Quotient: 4a + 5
Remainder: 16
If f(a) = 4a2 – 3a + 6, find f(2)
f(2) = 4(2)2 – 3(2) + 6
= 16 – 6 + 6 Remainder Theorem
= 16 If a polynomial f(x) is
divided by x – a , the
remainder is equal to f(a)

2. If find f (4).
Method 1 Method 2
Direct Substitution Synthetic Substitution
3 10 41 164 654
f (4) = 654. f (4) = 654

3. If find f(3).
3 2 -3 0 7
6 9 27
2 3 9 34
Answer: f(3) = 34

4. Show that is a factor of
Then find the remaining factors of the polynomial.
The remainder is 0, so x – 3 is
1 7 6 0 a factor of the polynomial
=

5. Show that is a factor of
Then find the remaining factors of the polynomial.
1 6 5 0

6. Geometry The volume of a
rectangular prism is given
by
Find the missing measures.
lwh =
1 9 20 0
The missing measures of the prism are x + 4 and x + 5.