1. Factoring

2. Factoring Trinomials of the Form
5.3
Factoring Trinomials of the Form
ax2 + bx + c, a = 1

3. Factoring Trinomials
Recall that factoring is the reverse process of multiplication. Using the FOIL method, we can show that
(x + 3)(x + 4) = x2 + 7x + 12.
Therefore x2 + 7x + 12 = (x + 3)(x + 4)
Note that this trinomial results in the product of two binomials whose first term is x and second term is a number (including its sign).

4. Factoring Trinomials Factoring any polynomial of the form x2 + bx + c
will result in a pair of binomials:
Numbers go here.
x2 + bx + c = (x +?)(x +?) O
( x + 3 )( x ) F I L
= x2 + 4x + 3x + 12
= x x

5. Factoring Trinomials Factor out a GCF if possible.
Find two numbers whose product equals the constant, c, and whose sum equals the coefficient of the x-term, b.
Use the two numbers found in step 2, including their signs, to write the trinomial in factored form.
Check using FOIL.

6. Examples – Factor each. x2 – 5x + 6 x2 + 2xy + y2 x2 + 8x + 15