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
Pull out the GCF
Find the greatest common factor of every term and factor it out first. This always simplifies the rest.
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.
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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