Factoring Quadratic Polynomials
We will now work in the opposite direction—factoring. First we will factor quadratic polynomials, expressions of the form ax2 + bx + c (where a is not 0). For example x2 + 5x + 6 is factored as (x + 2) (x + 3). Quadratic polynomials whose first factors are x2 are the easiest to factor. Their factorization always begins as (x ± _)(x ± _ ). This forces the first factor to be x2 when the FOIL method is used All you need to do is fill in the two blanks and decide when to use plus and minus signs. All quadratic polynomials factor though some do not factor ‘‘nicely.’’ We will only concern ourselves with ‘‘nicely’’ factorable polynomials in this chapter.
If the second sign
is minus, then the signs in the factors will be different (one plus and one
minus). If the second sign is plus then both of the signs will be the same. In
this case, if the first sign in the trinomial is a plus sign, both signs in the
factors will be plus; and if the first sign in the trinomial is a minus sign,
both signs in the factors will be minus.
Examples
Practice
Determine whether to
begin the factoring as (x + _) (x + _), (x – _)(x – _), or (x ± _)(x – _).
Solutions
Thanks for reading Factoring Quadratic Polynomials. Please share...!
