Question

The table below shows ordered pairs that belong to a polynomial function.



x f(x)
–1 –14
0 1
1 0
2 1




If
f
(
x
)
is a cubic polynomial, which conclusion is valid?


x
−
1
must be a factor of
f
(
x
)
.


x
+
1
must be a factor of
f
(
x
)
.


f
(
x
)
x
+
1
has a remainder of
14
.


f
(
x
)
x
+
2
has a remainder of
1
.

Answer 1

Correct conclusion: x − 1 must be a factor of f(x).

Reason: f(1) = 0, so by the Factor Theorem (or Remainder Theorem) x − 1 divides f(x).
The other choices are false: x + 1 is not a factor since f(−1) = −14 ≠ 0; the remainder on division by x + 1 is f(−1) = −14 (not 14); and the remainder on division by x + 2 would be f(−2), which is not given.