1Cademy - Strategy to Factor Polynomials Completely

Activity (Process)

Strategy to Factor Polynomials Completely

When factoring a polynomial, a systematic three-step strategy guides the selection of the correct method:

Step 1 — Is there a greatest common factor? Always begin by checking whether all terms share a GCF. If one exists, factor it out.

Step 2 — Classify the polynomial by its number of terms and choose the appropriate method:

Binomial (two terms):
- 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.
Trinomial (three terms):
- Of the form $x^2 + bx + c$ ? Undo FOIL.
- Of the form $ax^2 + bx + c$ $a x^{2} + b x + c$ ?
  - If $a$ and $c$ are squares, check whether it fits the trinomial square pattern.
  - Use the trial and error or "ac" method.
More than three terms: Use the grouping method.