Question

When
p
(
x
)
=
9
x
4
−
45
x
3
+
37
x
2
+
x
+
2
is divided by
x
−
2
,
a student can determine the remainder by evaluating
p
(
2
)
.
What is the value of
p
(
2
)
?

Answer 1

By the Remainder Theorem the remainder is p(2). Compute:

9(2^4) − 45(2^3) + 37(2^2) + 2 + 2
= 9(16) − 45(8) + 37(4) + 4
= 144 − 360 + 148 + 4
= -64.

So p(2) = -64.