First you must prove that this polynomial has no real roots.
(For any polynomial ax²+bx+c, the roots are $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$)
If it doesn't have real roots, it will always have the same sign as a, which is 4 in that case. 4 is positive, so the polynomial is positive for any real number x.)
First you must prove that this polynomial has no real roots.
(For any polynomial ax²+bx+c, the roots are $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$)
If it doesn't have real roots, it will always have the same sign as a, which is 4 in that case. 4 is positive, so the polynomial is positive for any real number x.)