Question

Factorise the following expressions.

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

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

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

Answer 1

$1)p^2+6p+8$

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

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

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

$2)q^2-10q+21$

$=q^{2}3q-7q+21$

$=q(q-3)-7(q-3)$

$=(q-3)(q-7)$

$3)p^2+6p-16$

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

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

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