Question

Factorise the following expressions.
$\left(i\right)p^2+6p+8\left(ii\right)p^2-10q+21\left(iii\right)p^2+6p-16$

Answer 1

$\left(1\right)p^2+6p+8$

$=p^2+4p+2p+8$

$=p(p+4)+2(p+4)$

$=(p+4)(p+2)$

$\left(2\right)p^2-10p+21$

$=p^2-3p-7p+21$

$=p(p-3)-7(p-3)$

$=(p-3)(p-7)$

$\left(3\right)p^2+6p-16$

$=p^2-2p+8p-16$

$=p(p-2)+8(p-2)$

$=(p+8)(p-2)$