Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Polynomials, Exercise 6: Exam Practice

$\sqrt{2}$ is a polynomial of degree

If $p\left(x\right)=x^2-2\sqrt{2}x+1$, find the value of $p\left(2\sqrt{2}\right)$.

If $x+1$ is a factor of the polynomial $2x^2+kx$, then the value of $k$ is

$\left(x+1\right)$ is a factor of the polynomial

If $x+y+z=1, xy+yz+zx=-1$ and $xyz=-1$, find the value of $x^3+y^3+z^3$

Find the square root of $\left(x^2+4x+4\right)\left(x^2+6x+9\right)$.

Simplify $\frac{{\left(a^2-b^2\right)}^3+{\left(b^2-c^2\right)}^3+{\left(c^2-a^2\right)}^3}{{\left(a-b\right)}^3+{\left(b-c\right)}^3+{\left(c-a\right)}^3}.$

If $x={\left(2+\sqrt{5}\right)}^{1/2}+\left(2-\sqrt{5}\right){}^{1/2}$ and $y={\left(2+\sqrt{5}\right)}^{1/2}-\left(2-\sqrt{5}\right){}^{1/2}$, evaluate $x^2+y^2$.