factor of m^5+m^4+m^3+m-4

Question

factor of m^5+m^4+m^3+m-4

Answer 1

Notice that m = 1 is a zero of this expression, i.e. m - 1 is a factor.

If you divide the expression by m-1, the quotient (other factor) is

m⁴ + 2m³ + 3m² + 3m + 4

If you graph the original expression, you will see that it has only one real root; therefore, the quotient cannot be factored further.