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

Answer:

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