The polynomial $p(x)=x^{4}-2 x^{3}+3 x^{2}-a x+3 a-7$ when divided by $x+1$ leaves the remainder $19 .$ Find the values of $a .$ Also find the remainder when $p(x)$ is divided by $x+2.$
Classify the following polynomials as polynomials in one variable, two variables etc.
$x y+y z+z x$
If $a+b+c=5$ and $a b+b c+c a=10,$ then prove that $a^{3}+b^{3}+c^{3}-3 a b c=-25.$
Expand
$(x+5 y)(x-5 y)$
Factorise the following quadratic polynomials by splitting the middle term
$x^{2}+2 x-143$