Factorise and divide the following: |
(a)\[\left( {{x}^{2}}-22x+117 \right)\div \left( x-13 \right)~~~~\] |
(b) \[\left( 9{{x}^{2}}-4 \right)\div \left( 3x+2 \right)\] |
Answer:
(a) \[({{x}^{2}}-22x+117)\div (x-13)\] \[\because \]\[{{x}^{2}}-22x+117={{x}^{2}}-(13+9)x+117\] \[={{x}^{2}}-13x-9x+117\] \[=x(x-13)-9(x-13)\] \[=(x-13)(x-9)\] \[\therefore \] \[\frac{{{x}^{2}}-22x+117}{(x-13)}=\frac{(x-13)(x-9)}{(x-13)}=x-9\] (b) \[~\left( 9{{x}^{2}}-4 \right)\div \left( 3x+2 \right)\] \[\because \] \[9{{x}^{2}}-4={{(3x)}^{2}}-{{(2)}^{2}}\] \[=\left( 3x+2 \right)\left( 3x-2 \right)\] \[\therefore \] \[\frac{9{{x}^{2}}-4}{(3x+2)}=\frac{(3x+2)(3x-2)}{(3x+2)}=(3x-2)\]
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