Question

Find k such that f(x)=x^4 + kx^3+2 has the factor x+1

Answer 1

Is the right answer k=1? If so, how do you get that algebraically?

Answer 2

Use the remainder theorem. If P(x) has a factor x+1, then P(-1)=0. So,
\[(-1)^4+k(-1)^3+2=0\Rightarrow k=3\]

Answer 3

??? sorry it didn't go through @John_ES

Answer 4

The problem says the polynomy f(x) must have a factor x+1, right?

Answer 5

Oh, ok.

Answer 6

Thanks!