Question

I'm trying to find the degree and determine all the roots for p(×)=5(x+4)(5x^2+4x+20)

Answer 1

A polynomial is of degree n if its largest term is x^n.

The polynomial

`p(x)=5(x+4)(5x^2+4x+20)`

is of degree 3 (because x * x^2 = x^3) and has two parts: (x+4) and (5x^2+4x+20)​.

The first part x+4 has roots at x = - 4, the second part does not have any real roots (the discriminant is < 0 ); therefore, the only real roots this polynomial has is x =-4.