I need help about a poly descomposition: [(x^2-x-21)/(2x^3-x^2+8x-4)]

[marcelinejinx]

First, sry for my english, well, i have the polynomial [(x^2-x-21)/(2x^3-x^2+8x-4)], and the book says that the denomitor can be transformed to:
(x^2+4)*(2x-1)

Anyone can explain me how did it? thank you so much <3

 

[tkhunny]

First, sry for my english, well, i have the polynomial [(x^2-x-21)/(2x^3-x^2+8x-4)], and the book says that the denomitor can be transformed to:
(x^2+4)*(2x-1)

Anyone can explain me how did it? thank you so much <3

Various ways exist to go about it.

What do you know of the Rational Root Theorem?

Is your Synthetic Division all practiced up?

 

[Dr.Peterson]

First, sry for my english, well, i have the polynomial [(x^2-x-21)/(2x^3-x^2+8x-4)], and the book says that the denomitor can be transformed to:
(x^2+4)*(2x-1)

Anyone can explain me how did it? thank you so much <3

They probably expect you to factor 2x^3-x^2+8x-4 by grouping. Are you familiar with that method (factor the GCF from each pair, then from the two factored forms)?