Question

If the polynomial $3x^4-4x^3-3x-1$ is divided by $x-1$, then the remainder is :

• A. 1
• B. 3
• C. 5
• D. -5

Answer 1

Answer: (D)

-5

For finding the remainder, we need to use remainder theorem

let $p\left(x\right)=3x^4-4x^3-3x-1$

Hence, to find the remainder on dividing by $x-1$, we need to equate it to 0 and put that value of $x$ in $p\left(x\right)$

$\Rightarrow p\left(x\right)=3x^4-4x^3-3x-1$

$\Rightarrow x-1=0$

$\Rightarrow x=1$

$\Rightarrow p\left(1\right)=3{\times 1}^4-4{\times 1}^3-3\times 1-1$

$\Rightarrow p\left(1\right)=-5$