Factor the polynomial 3x^3 + 2x^2 - 7x + 2 completely using the following steps.
1) Explain the connection between the roots of a polynomial and its factors
2) Find a root of the given polynomial by guessing or by trial-and-error
3) Using the root you found above give a factor of the polynomial
4) Divide the polynomial by the factor you found to demonstrate that it is a genuine factor and obtain its remaining factor
5) Factor the remaining factor you got above completely and give a complete factorization of the whole polynomial.
1) Explain the connection between the roots of a polynomial and its factors
2) Find a root of the given polynomial by guessing or by trial-and-error
3) Using the root you found above give a factor of the polynomial
4) Divide the polynomial by the factor you found to demonstrate that it is a genuine factor and obtain its remaining factor
5) Factor the remaining factor you got above completely and give a complete factorization of the whole polynomial.