Basics of Polynomials

Divide

$\left(x^3+x^2-2x+1\right) ÷\left(x+3\right)$

Person $A$ is $26$ years older than person $B$. The product of their ages (in years), $3$ years from now will be $360$. Find the present ages of person $A$ and person $B$.

A graph of a cubic polynomial is plotted on a graph paper.

The graph of a polynomial shows it is extended on both sides. What does it indicate about the values of the $y$ coordinate?

$p\left(x\right)={\left(x+3\right)}^2-2\left(x-c\right)$; where $c$ is a constant. If $p\left(x\right)$ is divisible by $x$, find the value of $c$. Show your steps.

If $a^2=by+cz; b^2=cz+ax; c^2=ax+by;$ the the value of $\frac{x}{a+x}+\frac{y}{b+y}+\frac{z}{c+z}$

If $x+y+z=0$, then the value of $\frac{\left(x+y\right)\left(y+z\right)\left(z+x\right)}{xyz}+11$ is

Consider the expression $x^{(m^2-1)} + 3x^{\frac{m}{2}}$, where $m$ is a constant. For what value of $m$, will the expression be a cubic polynomial?

A polynomial $p\left(x\right)$ of degree $n$, the graph of $y=p\left(x\right)$ intersects the $x-$axis at most $1$ points.

A polynomial $p\left(x\right)$ of degree $n$, has at most $n$ zero.

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 $3x^2 – 6x + x^3 – 18$

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

Factorise

$12a^2+2a-4$

Factorise

$4y^2+24y+20$

Factorise

$2a^2+7ab-15b^2$

Factorise

$1-t-6t^2$

Factorise

$6-9e-27e^2$

Factorise

$40y^2+y-6$

Factorise

$13k^2+37k-6$