How do I factor: 2x^4+x^3-8x^2-x+6?

Question

anonymous · Answer

do you know remainder and factor theorem?

anonymous · Answer

what do you mean?

anonymous · Answer

I can solve this question through it but need to know whether you know it or not?

anonymous · Answer

i guess not since I haven't heard of factor theorem.. I mean I know the special ones like difference of perfect square, cubes

anonymous · Answer

http://www.wolframalpha.com/input/?i=factor+2x^4%2Bx^3-8x^2-x%2B6

anonymous · Answer

i need steps-- I just don't get it

anonymous · Answer

2x^4+x^3-8x^2-x+6=0
2x^4+x^3-8x^2-x=-6
x(2x^3+x^2-8x-1)=-6 i don't know if it is correct

anonymous · Answer

$$f(x)=2x ^{4}+x ^{3}-8x ^{2}-x+6$$
Let x be 1,
f(1)=0
hence (x-1) is the factor.
Do you know this method?

anonymous · Answer

i've seen it before

anonymous · Answer

great.As we know that (x-1) is the factor,the equation can be wrote like this:
 (x-1)(Ax3+Bx2+Cx+D)=2x4+x3−8x2−x+6
please find the value of A,B and C and tell me the answer?

anonymous · Answer

why is x-1 the factor?

anonymous · Answer

because when x=1 then f(x)=0 and this proves that (x-1) is the factor.