Factoring Expectation: A1.1.3: Factor algebraic expressions.

Common Factors The first thing to look for in any factoring situation is a common factor among all of the terms of the polynomial. ex: 4x 3 + 8x 2 – 16x + 32

Product/Sum If x 2 + bx + c factors neatly, it factors into (x+d)(x+e) where d + e = b and de = c.

Factor the following: x 2 + 8x + 15 x 2 – 7x + 12 x x - 11

Factor the following: x 2 – 4x - 21 x 2 + x x x - 72

Factor the following: x 2 – 49 3x 2 - 3x x 3 – 6x 2 – 2x

Difference of Squares a 2 – b 2 = (a + b)(a – b) ex: x 2 – 36 = (x + 6)(x – 6) 4x 2 – 100 = (2x + 10)(2x – 10)

Sum of Squares The sum of 2 perfect squares does not factor. x is prime 10x is prime

Factor the Following x 2 – 64 27x

Completing the Square Sometimes it is helpful to modify a trinomial that is not factorable, so that we can factor it. Finding centers and the radius of a circle or the vertex and symmetry line for a parabola are 2 such situations. Completing the square allows us to do that.

Completing the Square 1. Group the x 2 and x terms in a quantity (x 2 + bx). 2. Add ( b / 2 ) 2 inside the quantity and subtract it outside. 3. x 2 + bx + ( b / 2 ) 2 factors into (x + ( b / 2 )) 2

Factor by completing the square. x 2 – 6x + 21

Factor by completing the square. x 2 + 8x - 20

Factor by completing the square. x x - 10

Factor by completing the square. x 2 –12x - 13

Factor by completing the square. x 2 – 5x - 4

Solve x 2 + 6x = 47 by completing the square.

What is the center and radius of the circle with equation x 2 – 4x + y y = 0