Four zeros
Explanations:The given equation is given as:
[tex]f(x)=x(x^3+1)+6x^2-8x[/tex]The function f(x) can be expanded to give:
[tex]\begin{gathered} f(x)=x^4+x+6x^2-8x \\ f(x)=x^4+6x^2-7x \end{gathered}[/tex]Note:
The zeros of a polynomial are the values of x that will make the function f(x) to be zero. This means that if those values (the zeros) are substituted into the function f(x), we will get 0 as the answer.
The number of zeros in a polynomial is the order of the polynomial
Therefore, the highest degree of the function f(x) above is 4, this means that the function f(x) has 4 zeros
