How do you factor the expression #5x^9+10x^8-15x^7+10x^6#?

1 Answer
Mar 2, 2016

Answer:

Separate out the common factor #5x^6# to find:

#5x^9+10x^8-15x^7+10x^6=5x^6(x^3+2x^2-3x+2)#

Explanation:

All of the individual terms are divisible by #5x^6#, so separate out that common factor to find:

#5x^9+10x^8-15x^7+10x^6=5x^6(x^3+2x^2-3x+2)#

The remaining cubic factor has no simpler factors with rational coefficients. In fact it has one irrational Real zero and a pair of Complex conjugate zeros. It is possible to find the zeros using Vieta's substitution or my favourite, Cardano's method, but this is probably beyond the scope of the question.