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