Summary: After performing synthetic division, if the remainder is zero, the binomial is a factor of the polynomial. After performing synthetic division, if the remainder is not zero, the binomial is not a factor of the polynomial.
Factoring a Four Term Polynomial
Group the first two terms and the last two terms together.
Find the GCF in both sets of parenthesis. What remains in the parenthesis after simplifying should be exactly the same for both sets.
One of the factors is what remains (you will only write this factor once even though you see it "twice"). The second factor comes from the GCF's of both sets.
If you are left with a difference of squares binomial as one of your factors, simplify the binomial down to its two factors.
Factoring a Three Term Polynomial with Descending Exponents
Factor out the GCF from all three terms. This should leave you with a three term quadratic expression.
Factor the quadratic using the British Method or the Box Method.
Factoring a Three Term Polynomial with Missing Exponents
Factor these equations as if they were quadratic equations. Rather than using an "x" with your factors, use an x^2. Refer to the video below.