question_answer

                       Factorise the following :

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

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

Answer:

(a)    \[18+\text{11}x+{{x}^{2}}=\text{ }{{x}^{2}}+1\text{1}x+18\]

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

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

\[=x(x+9)+2(x+9)\]

= (x + 9) (x + 2)

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

\[={{y}^{2}}-5y+3y-15~\] \[=y\left( y-5 \right)+3\left( y-5 \right)\]

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