The Deep Check

You check a factoring by multiplying the factors back. When there are several factors, multiply in stages. Take $x^{3}+3x^{2}+2x = x\left(x+1\right)\left(x+2\right)$. First multiply the parentheses: $\left(x+1\right)\left(x+2\right) = x^{2}+3x+2$. Then multiply by the $x$ in front. The result is the original cubic.

Start with the parentheses, then multiply by the factor in front. Compare the constant and each coefficient with the original expression. If anything differs, check the factor pair again, and check the common factor you took out.

When an expression was factored in several steps, check each step by multiplying. The final expansion must give back every term of the original expression.