Factoring When Terms Have a Common Factor
The polynomials we consider most when factoring are those with more than one term. To multiply a monomial and a polynomial with more than one term, we multiply each term of the polynomial by the monomial using the
distributive laws:
a(b + c) = ab + ac and a(b – c)= ab – ac.
To factor, we do the reverse. We express a polynomial as a product using the distributive laws in reverse:
ab + ac = a(b + c) and ab – ac = a(b – c).
TIPS FOR FACTORING
a. Before doing any other kind of factoring, first try to factor out the GCE.
b. Always check the result of factoring by multiplying.