question_answer

Factorise the following :

(a) \[18+11x+{{x}^{2}}\]

(b) \[{{y}^{2}}-2y-15\]

Answer:

(a)  \[18+11x+{{x}^{2}}=\text{ }{{x}^{2}}+\text{11}x+18\]

\[={{x}^{2}}+\left( 9+2 \right)\text{ }x+18\]

\[={{x}^{2}}+\text{ }9x+2x+18~\]

\[=x\text{ (}x+9)+2\text{ }\left( x+9 \right)\]

\[=\left( x+9 \right)\text{ (}x\text{ }+\text{ }2)\]

(b)  \[{{y}^{2}}-2y-15={{y}^{2}}-(5-3)y-15\]

\[={{\text{y}}^{2}}-5y+3y-15\]

\[=y\left( y-5 \right)+3\left( y-5 \right)~\]

\[=\left( y-5 \right)\left( y+3 \right)~\]