Jitender Gupta and Divya Malik Solutions for Exercise 4: CHAPTER EXERCISE

Using remainder theorem, find the remainder when  $f\left(x\right)=3x^4+2x^3-\frac{x^2}{3}-\frac{x}{9}+\frac{2}{27}$  is divided by $g\left(x\right) =\left(x+\frac{2}{3}\right)$.

When  $x^3-3x^2-kx+4$  is divided by $(x -3)$, then the remainder is $k$. Find the value of the constant $k$.

When divided by $(y-2)$, the polynomials  $p{y}^3+3y^2-13$ and $2y^3- 5y+p$ leaves the same remainder. Find the value of $p$.

The polynomials $3x^3-a{x}^2+5x-13$ and $(a+1)x^2-7x+5$ leaves the same remainder when divided by $(x -3)$. Find the value of $a$.

What number must be added to  $2x^3-7x^2+ 2x$, so that the resulting polynomial leaves the remainder $-2$ when divided by $(2x -3)$?

Find the value of constants $a and b$, $\left(x-2\right) and \left(x+3\right)$ are both factors of the expression $x^3+a{x}^2+bx-12$.

Find $b and c$ such that, $\left(y+1\right) and \left(y+2\right)$ are the factors of the polynomial $y^3+b{y}^2-cy+10$.

$(x-2)$ is a factor of expression $x^3+a{x}^2+bx+6$. When this expression is divided by $(x -3)$, it leaves the remainder $3$. Find the values of $a and b$.