Factorise the following quadratic polynomials by splitting the middle term
$x^{2}-12 x+20$
$(x-2)(x-10)$
Factorise
$\frac{4 x^{2}}{9}-\frac{x}{3}+\frac{1}{16}$
If both $x-2$ and $x-\frac{1}{2}$ are factors of $p x^{2}+5 x+r,$ show that $p=r$
Without actual division, prove that $2 x^{4}-5 x^{3}+2 x^{2}-x+2$ is divisible by $x^{2}-3 x+2$
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 $x+2.$
Simplify $(2 x-5 y)^{3}-(2 x+5 y)^{3}$
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