Final answer:
In mathematics, to determine factorability, identify a greatest common factor, use certain factoring techniques, check for patterns in polynomials, and verify the reasonableness of the answer.
Step-by-step explanation:
To determine if something is factorable in mathematics, first look for a greatest common factor that can be taken out from all terms. After that, you can apply different factoring techniques such as the difference of squares, trinomials, or factor by grouping. In each case, you'll attempt to break down the expression into a product of simpler expressions where the operands multiply to give the original terms, and their addition or subtraction result matches the middle term in the expression, if applicable. When dealing with polynomials, check if the polynomial is a perfect square or has a pattern that matches recognizable factoring forms.
As you practice more with various algebraic expressions, you'll get a better sense for when an expression is likely factorable. This 'factor intuition' is often followed by using algebraic rules to confirm if the expression can be factored or not. You might also multiply both sides by the same factor, eliminate terms wherever possible, and always check if the answer is reasonable in terms of magnitude, direction, sign, and units.