simplify: (x^3+5x^2+5x-2)/(x+2)

Question

i need to know how to solve this problem

Answer 1

It's likely that x+2 is a factor of the polynomial, so put x=-2 (the root corresponding to the factor) and, sure enough, it's a zero of the cubic expression (-8+20-10-2=0).
We can divide using algebraic or synthetic division. We get x^2+3x-2. This doesn't factorise rationally any further, so this quadratic expression is the simplification.