Precalculus · Problem 3.3.24

This is a quadratic in disguise—notice that $f(x)$ contains only even powers of $x$. If you substitute $u = x^2$, you get a standard quadratic in $u$ that you can factor or solve. Once you find the values of $u$, remember that each positive $u$ gives you two real values of $x$ (positive and negative), and the exponent on each factor tells you the multiplicity of that zero.

This is a quadratic in disguise—notice that $f(x)$ contains only even powers of $x$. If you substitute $u = x^2$, you get a standard quadratic in $u$ that you can factor or solve. Once you find the values of $u$, remember that each positive $u$ gives you two real values of $x$ (positive and negative), and the exponent on each factor tells you the multiplicity of that zero.