Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Polynomials, Exercise 3: Exercise 2.3

Using remainder theorem, find the value of $k$, so that $\left(4x^2+kx-1\right)$ leaves the remainder $2$, when divided by $\left(x-3\right)$.

The polynomials $x^3+2x^2-5ax-8$ and $x^3+a{x}^2-12x-11$, when divided by $\left(x-2\right)$ and $\left(x-3\right)$ respectively, leave remainders $p$ and $q$. If $q-p=10$, find the value of $a$.

Find the value of $a$, so that the polynomial $x^3-a{x}^2+13x+15$, when divided by $\left(x-1\right)$, gives $2$ as the remainder.

By actual division, find quotient and remainder, when $3x^4-4x^3-3x-1$ is divided by $x+1$. Also, verify remainder (by remainder theorem).

Find the quotient and remainder, when $6x^4+11x^3+13x^2-3x+27$ is divided by $3x+4$. Also, check the remainder obtained by using remainder theorem.

If the polynomials $2x^3+a{x}^2+3x-5$ and $x^3+x^2-2x+a$ leave the same remainder, when divided by $x-2$, find the value of $a$. Also, find the remainder in each case.

Check whether the polynomial $p\left(x\right)=9x^3-3x^2+x-5$ is a multiple of $\left(x-\frac{2}{3}\right)$.

Check whether the polynomial $p\left(x\right)=2x^4-4x^3+5x^2-3x-14$ is a multiple of $\left(x+1\right)$.