Factorise using factor theorem : $x^{3} - 6 x^{2} + 11 x - 6$ If angles A,B,C and D of the quadrilateral taken in order?

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Solution

$\begin{matrix} w e h a v e e q u^{n} : x^{3} - 6 x^{2} + 11 x - 6 i f p u t t h e v a l u e o f x i n e q u^{n}, x = 0, \Rightarrow 0 - 0 + 0 - 6 \neq 0 x = 1, \Rightarrow 1 - 6 + 11 - 6 = 0, 0 = 0 (x - 1) i s f a c t o r o f x^{3} - 6 x^{2} + 11 x - 6 x = 2, \Rightarrow 8 - 24 + 22 - 6 = 0, 0 = 0 (x - 2) i s f a c t o r o f x^{3} - 6 x^{2} + 11 x - 6 x = 3, \Rightarrow 3^{3} - 6 \times 3^{2} + 11 \times 3 - 6 = 0 \Rightarrow 27 - 54 + 33 - 6 = 0 \Rightarrow 60 - 60 = 0 (x - 3) i s f a c t o r o f x^{3} - 6 x^{2} + 11 x - 6 x^{3} - 6 x^{2} + 11 x - 6 = (x - 1), (x - 2), (x - 3) \end{matrix}$

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