M L Aggarwal Solutions for Exercise 1: Exercise 6

Find the remainder (without division) on dividing $f\left(x\right)$ by $(x-2)$where $f\left(x\right)=5x^2-7x+4$.

Find the remainder (without division) on dividing $f\left(x\right)$ by $(x-2)$where 
$f\left(x\right)=2x^3-7x^2+3$

Using remainder theorem, find the remainder on dividing $f\left(x\right)$ by $(x+3)$ where
 $f\left(x\right)=2x^2-5x+1$
 

Using remainder theorem, find the remainder on dividing $f\left(x\right)$ by $(x+3)$ where
 $f\left(x\right)=3x^3+7x^2-5x+1$
 

Using the remainder theorem, find the value of $k$, if on dividing $2x^3+3x^2-kx+5$  by $x-2$, leaves a remainder $7$
 

 Use factor theorem to factorise the following polynomials completely :
$x^3-13x-12$
.

 If $(x-2)$ is a factor of $2x^3-x^2-px-2$, then find the value of $p$.
 

What number should be subtracted from $2x^3-5x^2+5x$ so that the resulting polynomial has $2x-3$ as a factor?