last one i need help with

A value of k such that x - 1 is a factor of
x^3 - 2x^2 + 3x + k
is k =

a. -18
b. -6
c. -2
d. 1
e. 6
f. 22
g. none of these

should i plug the answer into the equation?

If (x−1) is a factor, then 1 is a root.
Let x=1. Set equal to 0 and solve for k.

would the answer be -2?

correct

pka said:

If (x−1) is a factor, then 1 is a root.
Let x=1. Set equal to 0 and solve for k.

Click to expand...

Just to clarify: You get roots "x = a" from solving factors "x - a = 0". So, given "x - 1" is a factor, then you would (at some point) solve for the related zero by setting the factor equal to zero and solving: x - 1 = 0, so x = 1. That is, when x = 1, you get "(polynomial) = (zero)". This is the basic relationship between factors and zeroes.

So if x - 1 is to be a factor of the listed polynomial expression, then x = 1 has to be a zero, so (1)³ - 2(1)² + 3(1) + k has to equal zero. Simplify, set the simplified expression (containing "k" and a number) equal to zero, and solve for "k=".

Eliz.