Factoring Polynomials

Algebra 2 Tutorial

Factoring Polynomials


Factoring polynomials is extremely important in your growth as a mathematician, but why? When we factor polynomials, we are finding the zeros of the function – meaning we are finding the places where the graph of the function crosses the x-axis.

Sample Problem

x^2 + 4x + 3






The first step in solving the problem is to make sure the polynomial is in standard form, which looks like:

ax^2 + bx + c

where a,b,and c are all real numbers. Luckily for us, this sample problem is already in standard form, so our next step is to take the constant term, the c term, and factor that term. In this problem, our c is 3, which produces only the factors 1 and 3. Our next step is to find which factors add up to form the b term. In this case, our only factors of the c term do indeed add up to our b term (3+1=4). Since we now have our factors, we must rewrite the original equation with the b term split up, giving us:

x^2 + 1x + 3x + 3

Now, we need to take out a greatest common factor from the two pairs of terms, which looks like this:

x(x+1) + 3(x+1)

Notice that the two parenthesis that are left unfactored are exactly the same, this is how you know you did it right. So our final answer is written in the form:


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