Basics of Polynomials

What is the possible expression for the third dimension of the cuboid $12k{y}^2+8ky-20k$, if the two of its dimensions are $(y-1)$ and $4k$?

The HCF of $(x^3+3x^2-x-3)$ and $(x^3+4x^2+x-6)$ is-

If f(x)= $4x^3-2x^2+5x-8$s divided by $(x – 2)$ then the remainder is

${\mathrm{x}}^2-5\mathrm{x}-6=$_____.

Which one is a factor of the following expression?

$x^2-11x+24$

Simplify the following expression:

$\left(4x^2-2x+8\right)-\left(x^2+3x-2\right)$

यदि $x^2+x-6=0$  तथा $x^2+6x+9=0$ हो तो $x$ बराबर होगा ?

${\mathrm{x}}^2+\mathrm{x}-20=$_____.

If $2x^2-7xy+3y^2=0$, then find the ratio of $x : y$.

The value of $t$for which $m^2-\frac{3}{2}m+t$ will be a perfect square, is

$6x^2-2-4x$ in the form of factors is

$5-x\left(6-x\right)$ in the form of factors is:

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.

Factorise: $(a-1)x^2-x-(a-2)$

What are bi-quadrinomials?

Write the following in standard form.
$4x^7+6x^2+28-3x^5-9x$

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