Use the matrix-column representation of the productto write each column of AB as a linear combination ofthe columns of A.

Week 2 Long Division: Example 1: 3 2 4 x −4x +x−1Remainder6 x+1 √x +0x −3x +0 x+5 4 3 −(4 x +4 x ) −4x −3x 2 3 2 −(−4x −4x ) x +0 x 2 −(x +x) −x+5 −(−x−1) 6 4 2 So 4x −3x +5 =4x −4x +x−1+ 6 x+1 x+1 Example 2: Factor x −2 x −5x+6 o Use trial and error to find a root x so that x −2 x −5x+6=0 o x=3 is a root, so x-3 is a factor x −2x −5x+6 2 o use long division to find that =x +x−2 x−3 o x −2 x −5x+6= x−( )x +x−2 ) ¿(x−3 )x−1 (x+2) Intervals & Inequalities: Simple examples: Interval Notation Number Line Inequality (a, b] a < x ≤ b (-∞, b) x ≤ b Inequalities in graphing example: Unions & Intersections: Given two sets A, B o Intersection A ∩ B = all objects in both A and B