Question

(5x power 2 - 19x + 12)÷(x-3) division​

Answer 1

Answer:

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)

Answer 2

$: \implies \frac{ {5x}^{2} - 19x + 12}{x - 3} \\ \\ : \implies \frac{ {5x}^{2} - 15x - 4x+ 12}{x - 3} \\ \\ : \implies \frac{ 5x(x - 3) - 4(x - 3)}{x - 3} \\ \\ : \implies \frac{ (5x - 4)(x - 3)}{ {(x - 3)}} \\ \\ 5x - 4$

Hope it's helpful to you