M L Aggarwal Solutions for Exercise 3: Chapter Test

Find the remainder when $2x^3-3x^2+4x+7$ is divided by $x-2$.

Find the remainder when $2x^3-3x^2+4x+7$ is divided by $2x+1$.

When $2x^3-9x^2+10x-p$ is divided by $\left(x+1\right)$, the remainder is $-24$. Find the value of $p$.

Use factor theorem to factorise the following polynomials completely:

$4x^3+4x^2-9x-9$ and $x^3-19x-30$

If $x^3-2x^2+px+q$ has a factor $\left(x+2\right)$ and leaves a remainder $9$ when divided by$\left(x+1\right)$, find the values of $p$ and $q$. With these values of $p$ and $q$, factorise the given polynomial completely.

If $\left(x+3\right)$ and $\left(x-4\right)$ are factors of $x^3+a{x}^2-bx+24$, find the values of $a$ and $b$. With these values of $a$ and $b$, factorise the given expression.

If $\left(2x+1\right)$ is a factor of both the expressions $2x^2-5x+p$ and $2x^2+5x+q$, find the values of $p$ and $q$. Hence, find the other factors of both the polynomials.

If a polynomial $f\left(x\right)=x^4-2x^3+3x^2-ax+b$ leaves remainders $5$ and $19$ when divided by $\left(x-1\right)$ and $\left(x+1\right)$ respectively, find the values of $a$ and $b$. Hence, determine the remainder when $f\left(x\right)$ is divided by $(x-2)$.