Question

If $x-1$ is a factor of $x^5-4x^3+2x^2-3x+k=0$, then $k$ is

• A. $4$
• B. $-4$
• C. $2$
• D. $3$

Answer 1

The correct option is A $4$

By factor theorem we know that,

If $x-a$ is a factor of $P\left(x\right)$, then $P\left(a\right)=0$

Hence if $x-1$ is a factor of $x^5-4x^3+2x^2-3x+k=0$

Then $1^5-4(1{)}^3+2(1{)}^2-3\left(1\right)+k=0$

$\Rightarrow 1-4+2-3+k=0$

$\Rightarrow k=4$