How we Solve Polynomial Equations Using Factoring ?
A polynomial equation is an equation that has polynomials on both sides. Polynomial equations can often be solved by putting everything on one side of the equation, then factoring the polynomial. For example, look at the equation
x^{2} - 2x- 3 = 0.
Everything is already on one side. If we factor, we get:
(x - 3)(x+1) = 0.
Look at what we have there: two things multiplied together give us zero. The only way that can happen is if one (or more) of the factors is zero to start with. In mathematical terms:
x - 3 = 0 or x + 1= 0.
Solving these equations yields
x = 3 or x = -1,
So these are the solutions of the original polynomial equation.
Remark: a second-degree equation never has more than 2 solutions. And an n^{th} degree equation never has more than n solutions.