Question

Divide 2x³-x²-2x-8 by x-2​

Answer 1

Answer:

Your equation is a fourth degree polynomial (aka a quartic) and thus we should be looking for four roots (although, of course, some might be duplicates).

From inspection, it should be (reasonably) obvious that one root is x=−1 , which means that (x+1) is a factor of the quartic expression. So, let’s factorise:

(x+1)(x3+x2+1)=0

Now, what are the roots of the cubic? I can’t see any obvious factors, so I could apply the formula for finding the roots of the generic cubic ax3+bx2+cx+d=0

x=q+q2+(r−p2)3−−−−−−−−−−−√−−−−−−−−−−−−−−−−√3+q−q2+(r−p2)3−−−−−−−−−−−√−−−−−−−−−−−−−−−−√3+p

where

p=−b3a

q=p3+bc−3ad6a2

r=c3a

Answer 2

hope it will  helps you