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

marcelinejinx

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Sep 10, 2018
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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
 
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?
 
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)?
 
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