# 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 $b$
5. Write the algebraic definition of the polynomial function graphed below.