MATH 140B Lecture Notes - Lecture 2: Polynomial
Document Summary
Def: a polynomial of degree n in the variable x of the form: F(x) = cnxn+ cn-1xn+1 + cn-2xn-2+ + c2x2+ c1x + c0. 3x2+2x-1 deg = 2, c2= 3, c1= 2, c0=-1. 4x5-x3+2x deg=5, c5= 4, c4=0, c3=-1, c2=0, c1=0. Def: a polynomial of degree u in variables x and y in the form: Cuxu+cu-1xu-1y + cu-2xu-2y2+ + c2x2yu-2+ c1xyu-2+ c0yu+ c x4y2+3x2y-4y5 deg= 5, var= x and y p3q-pq deg = 3, var= p and q. Elementary operation (for polynomial: add and subtract (collect like terms) (3x2+4+7x2+2x-1) + 2-x-x2-x3 = 6x3+2x2+x+5, scaler multiplication. 3(x+4) = 3x+3*4 = 3x+12: polynomial multiplication (dist) (3x-2)(x2+5x-1) = 3x3+15x2-3x-2x2-10x+2 = 3x3+13x2-13x+2. Special case product of 2 linear factors (x-2)(5x+4) = (x-2)5x+(x-2)4= 5x2+4x-10x-8 = 5x2-6x-8. Any integer can be written uniquely as the product of its prime factors. Any polynomial can be written uniquely as the product of its irreducible. What is true of p and q: 1. p+q=b.
