1. Factoring

2. Chapter Sections 5.1 – Factoring a Monomial from a Polynomial
5.2 – Factoring by Grouping
5.3 – Factoring Trinomials of the Form
ax2 + bx + c, a = 1
5.4 – Factoring Trinomials of the Form
ax2 + bx + c, a ≠ 1
5.5 – Special Factoring Formulas and a General Review of Factoring
5.6 – Solving Quadratic Equations Using Factoring
5.7 – Applications of Quadratic Equations
Chapter 1 Outline

3. Special Factoring Formulas and a General Review of Factoring

4. Difference of Two Squares
a2 – b2 = (a + b) (a – b)
Example:
a.) Factor x2 – 9.
x2 – 9 = x2 – 32 = (x + 3)(x – 3)
b.) Factor 16x4 – 9y4.
16x4 – 9y4 = (4x2)2 – (3y2)2 =
(4x2 + 3y2)(4x2 – 3y2)

5. Sum of Two Cubes a3 + b3 = (a + b) (a2 – ab + b2) Example:
a.) Factor x3 + 8.
x3 + 8 = x = (x + 2)(x2 – 2k + 4)

6. Difference of Two Cubes
a3 – b3 = (a – b) (a2 + ab + b2)
Example:
a.) Factor y
y3 - (5)3 = (y - 5)(y2 + 5y + 25)
b.) Factor 64p3 – q3.
64p3 – q3 = (4p)3 – (q)3= (4p – q)(16p2 + 4pq + q2)

7. Helpful Hint for Factoring
When factoring the sum or difference of two cubes, the sign between the terms in the binomial factor will be the same as the sign between the terms.
The sign of the ab term will be the opposite of the sign between the terms of the binomial factor.
The last term in the trinomial will always be positive.
a3 + b3 = (a + b) (a2 – ab + b2)
same sign
opposite sign
always positive
a3 – b3 = (a – b) (a2 + ab + b2)
same sign
opposite sign
always positive