Question

factorise 2x cube - 5 x square - 19 X + 42​

Answer 1

Answer:

hope it helps you.....

Answer 2

$2x^3 - 5x^2-19x+42 = (x-2)(x+3)(2x-7)$

Solution:

Given that, we have to factorize:

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

Substitute x = 2

$2(2)^3 - 5(2)^2 - 19(2) + 42\\\\16 - 20 - 38 + 42\\\\-4 + 4 = 0$

Thus, x - 2 is a factor

Now, the expression becomes,

$2x^3 - 5x^2-19x+42 = (x-2)(2x^2-x-21)\\\\Now\ factorize\ 2x^2-x-21$

$2x^2-x-21\\\\Split\ the\ middle\ term\\\\2x^2+6x - 7x - 21\\\\\mathrm{Break\:the\:expression\:into\:groups}\\\\\left(2x^2+6x\right)+\left(-7x-21\right)\\\\\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+6x\\\\\mathrm{Factor\:out\:}-7\mathrm{\:from\:}-7x-21\\\\Therefore\\\\2x\left(x+3\right)-7\left(x+3\right)\\\\\mathrm{Factor\:out\:common\:term\:}x+3\\\\\left(x+3\right)\left(2x-7\right)$

Thus the factors are:

$2x^3 - 5x^2-19x+42 = (x-2)(x+3)(2x-7)$

Learn more:

Factorize (256x^16 - 1)

https://brainly.in/question/2318326

(x-5)²-(5x-25)-24, Factorize the given polynomial.

https://brainly.in/question/4594371