Factorisation of Polynomials

If $\frac{{\left(x-3\right)}^2\left(x+3\right)}{2x-6}=p$, find the value of $2p$

Find the roots of the equation:

$6x^2-3-7x$

The factors of $x^3-x^{2}y-x{y}^2+y^3$, are

Factorise: $x^2-(2a+b)x+2ab$

Factorise : $x^3-x^2+ax+x-a-1$

Find the factors using the splitting middle term method.

$x^2+18x+32$

If $y= x^2-6x+2, x= 4-2y$, get a polynomial in $y$ and factorise it.

What is the factor of $x^2+x-2$

A rectangular park is to be designed whose breadth is $3 \mathrm{m}$ less than its length. Its area is to be $4 {\mathrm{m}}^2$ more than the area of the park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude $12 \mathrm{m}$. Find its length and breadth.

Evaluate: $\frac{\left(x-1\right)\left(x-2\right)\left(x^2-9x+14\right)}{\left(x-7\right)\left(x^2-3x+2\right)}$

How to find the factor of a polynomial?

Factorise: $y^3-y^2+ay+y-a-1$

Factorise $y²-5y+6$

Factorize: $5(2x-7y)-3(2x-7y{)}^2$

Factorise $p^2+10p+21$

Salma and Abid factorise the algebraic expression $p^4+9p^2+18$

Salma:

$p^4+9p^2+18=p^4+6p^2+3p^2+18$

$=p^2\left(p^2+6\right)+3\left(p^2+6\right)$

$=\left(p^2+3\right)\left(p^2+6\right)$

Abid:

$p^4+9p^2+18=p^4+6p+3p+18$

$=p(p+6)+3(p+6)$

$=\left(p^3+6\right)(p+6)(p+3)$

Who is correct? Give a reason to justify your answer.

Factorise :$12{\left(x^2+7x\right)}^2-8\left(x^2+7x\right)(2x-1)-15(2x-1{)}^2$

Factorise $a(a-1) - b(b-1)$.

If $x+1$is factor of $x^3+11x^2+15x+a$, then the value of $a$ is _____

$2x^2+10x-600=0$