Factoring

To factor a polynomial, first pull out any common factor shared by every term. Then factor what remains. For a trinomial like \(ax^2+bx+c\), find two numbers that multiply to \(ac\) and add to \(b\). Use those numbers to split the middle term, then factor by grouping: group the first two terms and the last two terms, factor each group, and pull out the shared binomial. For \(x^2+bx+c\), simply find two numbers that multiply to \(c\) and add to \(b\). A difference of squares \(a^2-b^2\) factors as \((a-b)(a+b)\).