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The factor theorem allows us to simplyfy the polynomial we have to solve once we know one solution and this might make the porblem easier to solve.
The factor theorem allows us to simplyfy the polynomial we have to solve once we know one solution and this might make the problem easier to solve.
There is also a similar theorem called the "remainder theorem". This states that if for some value of a, f(a) does not equal 0 then (x-a) cannot be a factor of f(x).
There is also a similar theorem called the "remainder theorem". This states that if for some value of a, f(a) does not equal 0 then (x-a) cannot be a factor of f(x).
==Generalizations==
==Generalizations==
===Polynomials in more than one variable===
===Polynomials in more than one variable===
Polynomials can be extended to be functions of more than one variable such as x and y. They are defined in the same way so all variables have integer powers greater than equal to 0. However there may be cross terms such as x<sup>2</sup>y<sup>3</sup>. In two variables, a generic polynomial can be expressed as:
Polynomials can be extended to be functions of more than one variable such as x and y. They are defined in the same way so all variables have integer powers greater than equal to 0. However, there may be cross terms such as x<sup>2</sup>y<sup>3</sup>. In two variables, a generic polynomial can be expressed as:
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