Question

Factorise 2x^3 - 5x^2 - 19x + 42​

Answer 1

Step-by-step explanation:

Answer:

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

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

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

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

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

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

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

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

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

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

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

Answer 2

Explantion:-

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

3

−4x

2

−x

2

+2x−21x+42

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

2

(x−2)−x(x−2)−21(x−2)

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

2

−x−2)

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

2

+6x−7x−21)

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

2

+6x−7x−21)

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

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

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

Ans.(x - 2)(2x - 7)(x + 3)