A polynomial equation is an equation where you are only allowed to add and subtract multiples of powers of a variable, like formula_3. An "n"th power is a variable multiplied by itself "n" times. Or example polynomial has 5th, 3rd, 2nd, and 1st powers of "x". The degree of a polynomial is the largest power found in the equation. In school, students learn about a type of polynomial equation called a quadratic equation. This is an equation where the highest power, or multiple, is two. An example of a quadratic equation isformula_4, or formula_5. Notice that the only thing we care about is that there is a squared term. This makes the equation quadratic. If formula_6 are numbers and formula_7, then formula_8 is a valid quadratic equation. You may remember from school that if you know formula_6 then you can solve this equation using the quadratic formula,formula_10which gives the solutions to our equation only by plugging in formula_6. Mathematicians hoped to find a simple equation for the solutions (or, roots) for "any" polynomial equation, hopefully using only addition, subtraction, multiplication, division, and two other simple calculations: powers and roots. Mathematicians were able, after years of work, to find equations for polynomials with degree 3, and eventually degree 4. However, no one was ever able to find a formula for the solutions to a polynomial with degree 5 or higher. Why not? What was preventing them from being able to plug in the (in this case, since there are 5 powers) formula_12 in formula_13 and get the answers? No one could find out why.