Basics of Polynomials

Is $8$ a polynomial?

Find the sum of two polynomials: $5x^3+3x^{2}y+4xy-6y^2, 3x^2+7x^{2}y-2xy+4x{y}^2-5$

Solve $3x^2 – 6x + x^3 – 18$

Factorise

$-18+a^2{b}^2-3ab$

The value of $27{\mathrm{a}}^3-2\sqrt{2}{\mathrm{b}}^3$ is equal to:

If $x=-2$ is one root of $x^3-x^2-17x=22,$ then find the other roots of equation.

$a{x}^n+bx+c$ is a quadratic polynomial if $n=?$

Examine the graph of the polynomial given below, write the nature of the polynomial. (Linear/Quadratic/Cubic).

Which of the following is a quadratic polynomial?

$\frac{1}{x}-1 \left(x\ne 0\right)$ is _____.

Find the value of $k$, if $x=3$ is a root of the equation $k{x}^2-10x+3=0$.

Write the degree of the polynomial $f\left(x\right)=x^2-3x^3+2$.

Write the degree of the polynomial $p\left(x\right)=2x^2-x^3+5$

If $P\left(x\right)=x^4+1$, then find $P\left(2\right)-P\left(-2\right)$.

Zeroes of the quadratic polynomial $x^2-2x-8$ are :

The degree of a linear polynomial is

Find the factor and solve the fourth degree polynomial:

$x^4-5x^2+4$

Factorise $a^4-11a^2+10$.

Factorise $(x^2+3x{)}^{2 }-3(x^2+3x)-4$.

Factorise $6x^{2}y-xy-2y$.