If you choose, you could then multiply these factors together, and you should get the original polynomial (this is a great way to check yourself on your factoring skills). One set of factors, for example, of 24 is 6 and 4 because 6 times 4 = 24. When you have a polynomial, one way of solving it is to factor it into the product of two binomials.
You have multiple factoring options to choose from when solving polynomial equations:
For a polynomial, no matter how many terms it has, always check for a greatest common factor (GCF) first. Literally, the greatest common factor is the biggest expression that will go into all of the terms. Using the GCF is like doing the distributive property backward.
If the equation is a trinomial — it has three terms — you can use the FOIL method for multiplying binomials backward.
If it’s a binomial, look for difference of squares, difference of cubes, or sum of cubes.
Finally, after the polynomial is fully factored, you can use the zero product property to solve the equation.
Also::::
If a polynomial doesn’t factor, it’s called prime because its only factors are 1 and itself. When you have tried all the factoring tricks in your bag (GCF, backwards FOIL, difference of squares, and so on), and the quadratic equation will not factor, then you can either complete the square or use the quadratic formula to solve the equation. The choice is yours. You could even potentially choose to always use either completing the square or quadratic formula (and skip the factoring) to solve an equation. Factoring can sometimes be quicker, which is why it is recommended that you try it first.
