Use the remainder theorem to evaluate f(k), then determine if k is a factor.
f(x)=10x^3-41x^2+32x+20; 5/2
f(5/2) is the remainder when f(x) is divided by (x - 5/2)
This site can help:
http://calc101.com/webMathematica/long-divide.jsp
f(x)=10x^3-41x^2+32x+20; 5/2
This site can help:
http://calc101.com/webMathematica/long-divide.jsp