No. \(8\sqrt x + 7{x^2}\) is not a polynomial. Another way of writing \(\sqrt x\) is as \({x^{\frac{1}{2}}}\). This index is a fraction not a whole number. That is why this is not a polynomial.

We solve polynomials algebraically in order to determine the roots - where a curve cuts the \(x\)-axis. A root of a polynomial function, \(f(x)\), is a value for \(x\) for which \(f(x) = 0\).