Polynomials

1. Find the quotient and remainder when
f(x) = x
5 – x
4 – 4x
3 + 2x + 3
is divided by g(x) = x – 2. Make sure the quotient and remainder are clearly identified.
2. Let f be a quartic polynomial (ie. a polynomial of degree 4). Suppose that f has
zeros at -2, 1, 3, 4 and that f(0) = 4.
• Sketch a graph of f.
• If f(x) is written in the form
f(x) = A(x – a)(x – b)(x – c)(x – d) ,
then find the values of A, a, b, c, d.
3. Suppose that f(x) has (x – 2)2 and (x + 1) as its only factors.
• Sketch the graph of f.
• State all the zeros of f.

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