Polynomial Trouble

**phgao** · February 2nd 2006, 01:33 AM

Hi!

Is 3^x + 3 a polynomial?
On my sheet it is written as 3 superscript x + 3. Thanks!

Also there is another question thanks! :

A right square pyramid, vertex O, stands on a square base ABCD. The height is 15cm and base length is 10cm. Find:

a. the length of the slant edge : I got that: 5 root 11.
b. the inclination of a slant edge to the base : 64.76 degrees
c. the inclination of a sloping face to the base : 71.57 degrees
d. the madnitude of the angle between two adjacent sloping faces : I have no idea about this one! Please help it is the angle between the faces?! I can't picture it.

Thanks!

**phgao** · February 2nd 2006, 01:43 AM

To add to this some more polynomials...

Is 5x^1.5 + 1.5x - 3 a polynomial? Why/not? And can you explain what is the power of 1.5 mean? I dont think i understand.

Lasly, cos(5x + 1) is it a poly or not? Please explain!

Thanks so much!

**CaptainBlack** · February 2nd 2006, 02:31 AM

Originally Posted by phgao

Hi!

Is 3^x + 3 a polynomial?
On my sheet it is written as 3 superscript x + 3. Thanks!
Thanks!

Wikipedia's definition of a polynomial is:

"In mathematics, a polynomial is an expression in which constants and
variables are combined using (only) addition, subtraction, and multiplication.
Thus, 7x2+4x−5 is a polynomial; 2/x is not."

I would also add to this definition that only a finite number of
additions, subtractions, and multiplications are to be allowed, as otherwise
we will find we have allowed infinite series, which I am pretty sure is not
intended.

$3^3+3=x \times x\times x +3$ ,

So yes $3^3+3$ is a polynomial.

RonL

**CaptainBlack** · February 2nd 2006, 02:42 AM

Originally Posted by phgao

To add to this some more polynomials...

Is 5x^1.5 + 1.5x - 3 a polynomial? Why/not? And can you explain what is the power of 1.5 mean? I dont think i understand.

$x^{1.5}$ means $(\sqrt x)^3$ when $x \ge 0$ , and something more complicated otherwise.
As $\sqrt x$ is not a polynomial, $5x^{1.5} + 1.5x - 3$ is not a polynomial.

Lasly, cos(5x + 1) is it a poly or not? Please explain!

Thanks so much!

$\cos$ is not a polynomial so $\cos (5x + 1)$ is not a polynomial.

RonL

**CaptainBlack** · February 2nd 2006, 02:45 AM

Originally Posted by phgao

Hi!

Is 3^x + 3 a polynomial?
On my sheet it is written as 3 superscript x + 3. Thanks!

Also there is another question thanks! :

A right square pyramid, vertex O, stands on a square base ABCD. The height is 15cm and base length is 10cm. Find:

a. the length of the slant edge : I got that: 5 root 11.
b. the inclination of a slant edge to the base : 64.76 degrees
c. the inclination of a sloping face to the base : 71.57 degrees
d. the madnitude of the angle between two adjacent sloping faces : I have no idea about this one! Please help it is the angle between the faces?! I can't picture it.

Thanks!

Your second problem is different in nature to the first so you should repost
it as a seperate thread.

RonL

**phgao** · February 2nd 2006, 02:52 AM

Thanks!
can you explain why power of 1.5 is the same as what you have typed:

$ (\sqrt x)^3 $

Thanks

**CaptainBlack** · February 2nd 2006, 03:28 AM

Originally Posted by phgao

Thanks!
can you explain why power of 1.5 is the same as what you have typed:

$ (\sqrt x)^3 $

Thanks

First we need:

$\sqrt x=x^{1/2}$ ,

this is so that the law of indices works for fractional indices. We want:

$x^{1/2}x^{1/2}=x^{1/2+1/2}=x$

So $x^{1/2}=\sqrt x$ .

Again by the law of indices:

$(\sqrt x)^3=x^{1/2}x^{1/2}x^{1/2}=x^{1/2+1/2+1/2}=x^{1.5}$

RonL

**ThePerfectHacker** · February 2nd 2006, 10:52 AM

Originally Posted by phgao

Thanks!
can you explain why power of 1.5 is the same as what you have typed:

$ (\sqrt x)^3 $

Thanks

It actually is a definiton, not a theorem.
We define $x^{n/m}$ as $\sqrt[m]{x^n}$

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