Download Pre-Calculus - Shelbyville CUSD #4

Pre-Calculus
Section 3.4
The Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra- If f(x) is a polynomial of
degree n, where n > 0, then f has at least one zero in the complex
number system.
Linear Factorization Theorem- If f(x) is a polynomial of degree n,
where n > 0, f has precisely n linear factors f(x) = an(x – c1)(x – c2)…(x
– cn) where c1, c2, …, cn are complex numbers.
Find all of the zeros of the function.
1.
f(x) = x2(x + 3)
2.
f(x) = (x + 9)(x + 4i)(x – 4i)
Find all the zeros of the function and write the polynomial as a product
of linear factors. Use your factorization to determine the x-intercepts of
the graph of the function. Use a graphing utility to verify that the real
zeros are the only x-intercepts.
1.
f(x) = x2 – 12x + 26
2.
f(x) = x2 + 25
3.
f(x) = x4 + 10x2 + 9
4.
f(x) = x3 – 3x2 – 15x + 125
5.
f(x) = 5x3 – 9x2 + 28x + 6
6.
f(x) = x4 + 25x2 + 144
Find a polynomial function with real coefficients that has the given
zeros. (There are many correct answers.)
1.
2, i, -i
HW: p. 296-297 2, 4, 9-42 x 3
2.
0, -5, 1 + 2i