Question

find the value of k, if x - 1 is a factor of $4x^3 + 3x^2 - 4x + k$. -3 0 3 none of these

Explanation:

Step1: Apply Factor Theorem

If $x-1$ is a factor, then $f(1)=0$.

Step2: Define the polynomial

Let $f(x)=4x^3 + 3x^2 - 4x + k$.

Step3: Substitute $x=1$

$f(1)=4(1)^3 + 3(1)^2 - 4(1) + k$

Step4: Simplify the expression

$f(1)=4 + 3 - 4 + k = 3 + k$

Step5: Solve for $k$

Set $3 + k = 0$, so $k = -3$

Answer:

A. -3