Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Polynomials, Exercise 4: Exercise 2.4

Factorise $x^3+2x^2-5x-6$.

By using factor theorem, show that $\left(x-2\right)$ is a factor of the polynomial $2x^3-3x^2-17x+30$.

Show that $\left(x-1\right)$ is a factor of $4x^3+3x^2-4x-3$ by using factor theorem.

Determine whether $\left(x-2\right)$ is a factor of the polynomial $3x^4+4x^3-10x^2-5x-28$.

Show that $\left(x+5\right)$ is the factor of the polynomial $x^3+x^2+3x+115$.

Check whether $\left(-2x-5\right)$ is a factor of the polynomial $p\left(x\right)=3x^4+5x^3-2x^2-4$ or not.

If $\mathrm{a}{\mathrm{x}}^3\mathrm{}+\mathrm{}\mathrm{b}{\mathrm{x}}^2\mathrm{}+\mathrm{}\mathrm{x}\mathrm{}-\mathrm{}6$ has $\mathrm{x}\mathrm{}+\mathrm{}2$ as a factor and leaves a remainder $4$ when divided by $(\mathrm{x}\mathrm{}-\mathrm{}2)$, find the values of $\mathrm{a}$ and $\mathrm{b}$.

What must be subtracted from $4x^4-2x^3-6x^2+x-5$, so that the result is exactly divisible by $2x^2+x-1$?