Question

The value of $k$ for which $x-1$ is a factor of the polynomial $4x^3+3x^2-4x+k$ is

• A. $3$
• B. $0$
• C. $1$
• D. $-3$

Answer 1

Answer: (D)

$-3$

Given that, $(x-1)$ is a factor of $4x^3+3x^2-4x+k$

To find out: The value of $k$.

Let the given polynomial be $p\left(x\right)$.

According to the factor theorem, if $(x-a)$ is a factor of $f\left(x\right)$, then $f\left(a\right)=0$.

Therefore, by Factor theorem $p\left(1\right)=0$

$\Rightarrow 4(1{)}^3+3(1{)}^2-4\left(1\right)+k=0$

$\Rightarrow 4+3-4+k=0$

$\Rightarrow k=-3$

Hence, the value of $k$ is $-3$.