Factorise the following quadratic polynomials by splitting the middle term

$15 x^{2}+7 x-2$

If $(5 x-3)^{2}=25 x^{2}+k x+9,$ then find $k$

Write the following cubes in expanded form

$(4 x-3 y)^{3}$

From the following polynomials find out which of them has $(x-1)$ as a factor

$x^{3}+4 x^{2}+x-6$

With the help of the remainder theorem, find the remainder when the polynomial $x^{3}+x^{2}-26 x+24$ is divided by each of the following divisors

$x-4$