Mathematics
Factoring Polynomials
Factoring rewrites a polynomial as a product of simpler polynomials. The method depends on the form — start with the greatest common factor, then look for patterns like difference of squares or factorable trinomials.
How to Approach Factoring Polynomials
- 01
Pull out the GCF
Find the greatest common factor of every term and factor it out first. This always simplifies the rest.
- 02
Check for special patterns
Difference of squares (a² - b²) = (a-b)(a+b). Perfect square trinomial (a² ± 2ab + b²) = (a ± b)². Sum/difference of cubes have their own formulas.
- 03
Try grouping or the AC method
For four-term polynomials, group pairs. For trinomials ax² + bx + c with a ≠ 1, use the AC method: find two numbers that multiply to ac and add to b.
Frequently Asked Questions
Can every polynomial be factored?
Over the rationals, no — some are 'irreducible'. Over the complex numbers, every polynomial of degree n factors into n linear factors (Fundamental Theorem of Algebra).
What's the AC method?
For ax² + bx + c, find two numbers that multiply to ac and add to b. Split the middle term using those numbers, then factor by grouping.
How do I factor cubics?
Try the Rational Root Theorem first to find one linear factor, then polynomial-divide and factor the remaining quadratic. ScanSolve handles the whole pipeline.
Related Topics
More step-by-step guides in Mathematics and adjacent subjects.
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