Basics of Polynomials

Let $f\left(x\right)$ be a polynomial with integer coefficients satisfying $f\left(1\right)=5$ and $f\left(2\right)=7$. The smallest possible positive value of $f\left(12\right)$ is

Solve $3x^2 – 6x + x^3 – 18$

Let $n$ be a positive integer. The number of common factors of $n^2+3n+1$ and $n^2+4n+3$ is equal to

The value of the polynomial $f\left(x\right)=x^3-x^2+x-1$ when $x=1$ is

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 $n=?$

Which is the possible polynomial for the graph given below:

Graph of the polynomial given below can be

Seeing the graph given below, write its nature 

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 $p\left(x\right)=2x^2-x^3+5$

Consider the following two statements
$\mathrm{I}$. Any pair of consistent liner equations in two variables must have a unique solution.
$\mathrm{II}$. There do not exist two consecutive integers, the sum of whose squares is $365$ .

Then

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:

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