Manipur Board Solutions for Chapter: Polynomials, Exercise 2: EXERCISE 2.2

Use factor theorem to show that $x-2$ is a factor of $x^3-9x^2+26x-24$.

Use factor theorem to show that $x+y, y+z, z+x$ are the factors of ${\left(x+y+z\right)}^3-\left(x^3+y^3+z^3\right)$.

Use factor theorem to show that $x-y, y-z, z-x$ are a factors of $x^3\left(y^2-z^2\right)+y^3\left(z^2-x^2\right)+z^3\left(x^2-y^2\right)$.

Find the value of $k$, if $x-1$ is a factor of $p\left(x\right)=x^2-2x+k$ 

Find the value of $k$, if $x-1$ is a factor of $p\left(x\right)=\sqrt{2}{x}^2+kx-1$ 

Find the value of $k$, if $x-1$ is a factor of $p\left(x\right)=k{x}^2-\sqrt{2}x+1$

Find the value of $k$, if $x-1$ is a factor of $p\left(x\right)=k{x}^2-3x+2k$

If $x^2+px+q$ and $x^2+lx+m$ are both divisible by $x+a$, show that $a=\frac{m-q}{l-p}$