Embibe Experts Solutions for Exercise 1: SAT 2021

Let $P\left(x\right)$ be a polynomial of degree $3$ and $P\left(n\right)=\frac{1}{n}$ for $n=1,2,3,4$. Then the value of $P\left(5\right)$ is

${\left(x+1\right)}^4$ is divided by $(x-1{)}^3$. Then, the value of the remainder at $x=1$ is 

If $(ax+b)\left(x^5+1\right)-(5x+1)$ is divisible by $x^2+1$, then the value of $2a+3b$ is

For real numbers $p, q$ and $a$, if the polynomial $x^3-3px+2q$ is divisible by the polynomial $x^2+2ax+a^2$, then which
of the following is correct?