Question

Factorise 2x^3 - 5x^2 - 19x + 4​

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

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

Given polynomial is of 3 rd degree so

We Wii have 3 factors

let f(x) = 2x^3 -5x^2–19x +42

Try x= +— 1 or x=+ -2

By remainder theorem if remainder of polynomial is 0 for that particular value x=a then we can say that (x--a ) is a FACTOR of f(x)

Put x=2 in f(x)

f(2) = 16--20-38+42 =0

(x-2) is afactor of f(x)

Dividing f(x) by (x-2) long method or synthetic method we get

(2x^2-x--21)

Factors of f(x) given are

(x-2) ( 2x^2-x--21)

Factors of

2x^2---x-21 =

= 2x^2 --7x+6x-21

=x(2x--7) +3(2x--7)

= (x+3)(2x--7)

So the factors of the given polynomial are

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