Trigonometry Homework #2 due 2-16

  1. Find the unique polynomial P(x) which satisfies the below list of conditions and write it in the form P(x)=a_nx^n+\cdots+a_1x+a_0.
    • the degree is as small as possible
    • the coefficients are real
    • P(4)=0
    • P\left(\frac{-i}{3}\right)=0
    • P(0)=1
  2. Sketch a graph of f(x)=x^3-3x^2+4x-12.
  3. Re-write x^5+x^4+x^3+x^2-12x-12 as a product of linear factors.
  4. Given f(x)=ax^3-bx^2+3x+4 and the graph of f(x) below, find a and bucogydvo7k
  5. Write the algebraic definition of the polynomial function graphed below.6pd7zqmrch
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