Trinomials: x^2 + bx + c

When we're looking at a trinomial, it will show up in one of two general forms:

x2 + bx + c
OR
ax2 + bx + c

When we have the first form (there's an invisible 1 in front of the x2) remember to look for the 'signals':
    * If there's a negative in front of the c value, we know that the factor pieces are going to have DIFFERENT signs - if c is positive, then the factor pieces are going to have the SAME sign
    *  Look at b -->  if b is positive, then the larger factor will be positive - if b is negative, then the larger factor will be negative.
    * Make your X-Factor.  The product goes on top, and the sum goes on the bottom.  The sides are used to find the factors of the top that add up to the bottom (don't forget to keep those signals in mind!)
Ex:  x2 + 6x + 8

X-Factor

We know that the factor pairs of 8 are (1, 8) and (2, 4), and that the factors have to add up to 6.  Which one does that?  (2, 4)

From here, we combine our signals and our factor pair to find the following:
          (x + 2)(x +4)   <--- FACTORED FORM
    To double check, FOIL:   x2 + 4x +2x + 8
  and combine like terms:  x2 + 6x + 8  <-- is this the polynomial we started with?  Yup!  Our factored form is right!


Extra Practice with x2 + bx + c
http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Factoring%201.pdf