MAT 117
Quiz 6
Name ________________________________
Use pencil, please.
Place ANSWERS ONLY in the boxes.
1) If x + 3 is a factor of a polynomial, then
2) If 7 is a zero of a polynomial, then
3) If
3
is a zero of a polynomial, then
2
4) A polynomial of degree 8 can have as many as
Class Time ______________
is a zero.
is a factor.
is a factor. (Answer with INTEGER COEFFICIENTS)
zeros and as many as
local extrema.
5) Use the rational zeros theorem to find all possible rational zeros of the polynomial
P(x) = 6x7 – 14x6 + x5 – 235x4 + 46x2 – 9
6) Find THE EXACT VALUE of all zeros of the following polynomials.
Answer in fraction form (NO DECIMALS).
a) f(x) = x2 – 8x – 105
b) g(x) = 5x3 – 38x2 + 24x + 16
d) h(x) = 3x3 – 11x2 – 19x – 5
c) P(x) = x3 – 3x2 + x + 5
e) k(x) = 7x4 – 39x3 + 45x2 – x – 12
7) Find a third degree polynomial that has zeros of 2, 5, and –1, and passes through (3, 18).
Answer in factored form.
8) If 3 – 2i is a zero of a polynomial (with all real coefficients), then
is also a zero.
9) Find the polynomial with the following properties:
* All coefficients are integers, and the leading
coefficient is 1. 2 + i is a zero. 3 is a zero. The polynomial has degree 3. Answer in factored form.
10) Find the polynomial with the following properties:
* All coefficients are integers, and the leading
coefficient is 1. 3i is a zero with a multiplicity of 2. The polynomial passes through the origin.
The polynomial has degree 5. Answer in factored form.