Factor of f(x)

does
\(f(x)=2x^3-x^2+2x-3\) have a factor of \(x-1\)

you can check is two ways, either factor or use long division

1. factor it

\(f(x)=2x^3-x^2+2x-3 \)
\(f(x)=2x^3+x^2+3x-2x^2-x-3 \)
\(f(x)=(2x^3-2x^2)+(x^2-x)+(3x-3 )\)
\(f(x)=2x^2(x-1)+x(x-1)+3(x-1 )\)
\(f(x)=(x - 1) (2x^2 + x + 3)\)=> have a factor of \((x-1)\)

we will get same answer doing long division

 

Thank you. You see what I mean? I am crazy to think that I am ready for Calculus 1. This question is something I should be able to do with my eyes closed.