Question

Factorise 2x^3 - 5x^2 - 19x + 42

Answer 1

$\huge\underline\textsf{Question:- }$

$\boxed{\sf2x ^{3} - 5x {}^{2} - 19x + 42}$

$\huge\underline\textsf{Explantion:- }$

$\leadsto\sf\red{2x {}^{3} - 4x {}^{2} - x {}^{2} + 2x - 21x + 42}$

$\leadsto\sf\orange{2x {}^{2} (x - 2) - x(x - 2) - 21(x - 2)}$

$\leadsto\sf\purple{(x - 2)(2x {}^{2} - x - 2)}$

$\leadsto\sf\blue{(x - 2)(2x {}^{2} + 6x - 7x - 21)}$

$\leadsto\sf\pink{(x - 2)(2x {}^{2} + 6x - 7x - 21)}$

$\leadsto\sf\orange{(x - 2)[(2x(x + 3) - 7(x + 3)]}$

$\leadsto\sf\red{(x - 2)(2x - 7)(x + 3)}$

$\large\underline\textsf{\green{Ans.(x - 2)(2x - 7)(x + 3)} }$

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \pink{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline {\huge{ \sf{ \: \: TO \: \: FACTORISE : \leadsto \: }}}$

$\tt{ 2x {}^{3} - 5x {}^{2} - 19x + 42} \\ \\ \tt{ = 2x {}^{3} - (4x {}^{2} - x {}^{2} )+ (2x -21x )+ 42 }\\ \\ \tt{ = 2x {}^{3} - 4x {}^{2} - x {}^{2} + 2x -21x + 42} \\ \\ \tt{ = 2x {}^{2} (x - 2) - x(x - 2) - 21( x - 2)} \\ \\ \tt{ = (x - 2)(2x {}^{2} - x - 21) }\\ \\ \tt{ = (x - 2)[2x {}^{2} - (7 - 6)x - 21]} \\ \\ \tt{ = (x - 2)(2x {}^{2} - 7x + 6x - 21)} \\ \\ \tt{ = ( x - 2)[x(2x - 7) + 3(2x - 7)] }\\ \\ \tt{ = (x - 2)(x + 3)(2x - 7)}$