how to find roots,max and min of polynomial equations?

Question

Given y=(x+5)(x-1)²(x-7), what are the roots,max and min?

Answer 1

Polynomials of odd degree have no constant maximum or minimum.

 

Polynomials of even degree and leading coefficient positive have no maximum but do have an absolute minimum.

Polynomials of even degree and leading coefficient negative have no minimum but do have an absolute maximum.

 

The finding of roots is a subject covered thoroughly in Algebra II or College Algebra and involves factoring, graphing, quadratic formula, synthetic division, Descartes' rule of signs and the Rational Roots Theorem.  See a textbook.