Prep Qs for test

• Dec 11th 2008, 05:26 PM
Pineapple
Prep Qs for test
-Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros.
-3, -4 + i, 1-√3

Factor Polynomial completely
8c^3 - 512

Evaluate Expression
(1.5 x 10^4)(3.2 x 10^-8) <power of negative 8
(1.2 x 10^-7) <power of negative 7

-I could really use help on how to solve these. I have a test tomorrow and these are the main type of problems i didnt understand.
• Dec 12th 2008, 02:25 AM
mr fantastic
Quote:

Originally Posted by Pineapple
-Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros.
-3, -4 + i, 1-√3

Linear factors are $(z + 3)$, the conjugate pair $(z + 4 - i)$ and $(z + 4 + i)$ (since the conjugate root theorem is valid), and $(z - 1 + \sqrt{3})$. Therefore .....

I was tempted to add $(z - 1 - \sqrt{3})$ as a factor so that $z^2 - 2z - 2$ is a quadratic factor and you have a nice simple polynomial, but then the resulting polynomial is not of least degree.

Quote:

Originally Posted by Pineapple
Factor Polynomial completely
8c^3 - 512

$= 8(c^3 - 64) = 8(c^3 - 4^3)$ and I'm sure you know how to factorise a difference of two cubes.

Quote:

Originally Posted by Pineapple
Evaluate Expression
(1.5 x 10^4)(3.2 x 10^-8) <power of negative 8
(1.2 x 10^-7) <power of negative 7
[snip]

Both can be done using a calculator. What's actually required here? A technology free simplification (in which case nothing needs to be done with the second) .....?