Polynomials

Polynomials

1. 4x^6+3x^5+2x^2+5x-8

   • This is a polynomial of the degree 6
   • the coefficent of x^6 is 4
   • f(x) are the values of x where f(x)=0
     • where it crosses the x axis

2. Synethetic Division

   • Divide 2x^2+7+1 by x+2
     • x=-2 is the divisor
     • In the table the top line is the coefficents of the quoteint and the remeinder
     • The degreeof the quotient is one less than the degree of the polynomial
     • (x+2)(2x+3x)-5
   • Dividing by (ax-b)
     • rearange to a(x-b over a)
       • 2x-1=2(x-half)

3. Remainder Theorm

   • In generl if F(x) is divided by x-h the remainder is f(h)

4. Factor theorem

   • if f(h)=0 then x-h is a factor

5. sketching

   • The roots are the values that f(x)=0