Factorize: $2 x^{3} + 9 x^{2} + 10 x + 3$

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Solution

${2 x}^{3} + {9 x}^{2} + 10 x + 3 = {2 x}^{3} + {2 x}^{2} + {7 x}^{2} + 7 x + 3 x + 3 = {2 x}^{2} (x + 1) + 7 x (x + 1) + 3 (x + 1) = ({2 x}^{2} + 7 x + 3) (x + 1) = ({2 x}^{2} + x + 6 x + 3) (x + 1) = [x (2 x + 1) + 3 (2 x + 1)] (x + 1) = (x + 3) (2 x + 1) (x + 1)$
Thus finally we can write the above equation as follow :-
${2 x}^{3} + {9 x}^{2} + 10 x + 3 = (x + 3) (2 x + 1) (x + 1)$

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