Question

consider f(x)=x(x^3+1)+6x^2-8xHow many zeros does f have? how do you know?Describe the end behavior of f how do you know?

Answer 1

In a polynomial equation, the number of zeros its determined by the máximum exponent possible, in the equation.

So then, in this equation

first develope parenthesis, to eliminate it

then x (x^3 + 1) becomes x^4 + x

now add the other 2 terms to get

x^4 + x + 6x^2 -8x

then this equation should have 4 zeros

2nd part)

End behavior , how do you know

its the graph near x axis

First , it have a zero at x= 0

the second zero is at x= 1

it grows to infinity when x goes to infiniy

and grows to infinity when x goes to -infinity.