Question

question given f(x) = 3x³ + kx + 2, and x - 1 is a factor of f(x), then what is the value of k? answer attempt 1 out of 2

Explanation:

Step1: Apply Factor Theorem

If \(x - a\) is a factor of \(f(x)\), then \(f(a)=0\). Here, \(a = 1\) (since the factor is \(x - 1\)).

Step2: Substitute \(x = 1\) into \(f(x)\)

Given \(f(x)=3x^{3}+kx + 2\), substitute \(x = 1\):
\(f(1)=3(1)^{3}+k(1)+2\).
Simplify: \(f(1)=3 + k+ 2=k + 5\).
Since \(x - 1\) is a factor, \(f(1)=0\), so \(k + 5=0\).
Solve for \(k\): \(k=-5\).

Answer:

\(-5\)