Jitender Gupta and Divya Malik Solutions for Exercise 3: Topic Exercise

Using factor theorem, check whether the polynomial $g\left(x\right)=x-2$ is a factor of $f\left(x\right)=x^3-4x^2+x+6$ or not.

If $\left(x+2\right)$ and $\left(x+3\right)$ are the factors $x^3+ax+b$, find the value of $a+b$.

Find the value of $\text{'}k\text{'}$ if $\left(x-2\right)$ is a factor of $x^3+2x^2-kx+10$ . Hence, determine whether $\left(x+5\right)$ is also a factor.

For $a=\frac{k}{3}$, the polynomial $g\left(x\right)$ is a factor of $f\left(x\right)$, where $f\left(x\right)=x^3+a\left(x^2+1\right)-2x+4, g\left(x\right)=x+a$. Find $k$.

What must be subtracted from $16x^3- 8x^2+4x+7$, so that the resulting expression has $(2x + 1)$ as a factor?

Use factor theorem to factorise completely $x^3+x^2-4x-4$.

Use factor theorem to factorise the polynomial $x^3-13x-12$ completely. Hence, solve the corresponding polynomial equation.

If $(x -2)$ is a factor of the expression  $2x^3+a{x}^2+bx-14$  and when the expression is divided by $(x -3)$, it leaves a remainder $52$. Find the values of $a and b$.