Recognize and use the appropriate method to factor a polynomial completely
Before you get started, take this readiness quiz.
Factor
.
If you missed this problem, review
[link] .
Factor
.
If you missed this problem, review
[link] .
Factor
.
If you missed this problem, review
[link] .
Factor
.
If you missed this problem, review
[link] .
Recognize and use the appropriate method to factor a polynomial completely
You have now become acquainted with all the methods of factoring that you will need in this course. (In your next algebra course, more methods will be added to your repertoire.) The figure below summarizes all the factoring methods we have covered.
[link] outlines a strategy you should use when factoring polynomials.
Factor polynomials.
Is there a greatest common factor?
Factor it out.
Is the polynomial a binomial, trinomial, or are there more than three terms?
If it is a binomial:
Is it a sum?
Of squares? Sums of squares do not factor.
Of cubes? Use the sum of cubes pattern.
Is it a difference?
Of squares? Factor as the product of conjugates.
Of cubes? Use the difference of cubes pattern.
If it is a trinomial:
Is it of the form
? Undo FOIL.
Is it of the form
?
If
and
are squares, check if it fits the trinomial square pattern.
Use the trial and error or “ac” method.
If it has more than three terms:
Use the grouping method.
Check.
Is it factored completely?
Do the factors multiply back to the original polynomial?
Remember, a polynomial is completely factored if, other than monomials, its factors are prime!
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