question_answer

Factorise the following :

(a) \[{{x}^{2}}+9x+20\]

(b)\[{{p}^{2}}-13p-30\]

Answer:

(a) \[{{x}^{2}}+9x+20={{x}^{2}}+\left( 5+4 \right)\text{ }x+20\]

\[=\text{ }{{x}^{2}}+5x+4x+20\]

\[=\text{ }x\left( x+5 \right)+4\left( x+5 \right)\]

\[=\left( x+5 \right)\left( x+4 \right)\]

(b) \[{{p}^{2}}13p30={{p}^{2}}\left( 152 \right)\text{ }p30\]

\[={{p}^{2\text{ }}}15p+2p30\]

\[=\text{ }p\left( p15 \right)+2\text{ }\left( p15 \right)\]

\[=\left( p15 \right)\left( p+2 \right)\]