1. ## Polynomial Trouble

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

Thanks!

2. 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!

3. 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.

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

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

RonL

4. 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.
$\displaystyle x^{1.5}$ means $\displaystyle (\sqrt x)^3$ when $\displaystyle x \ge 0$, and something more complicated otherwise.
As $\displaystyle \sqrt x$ is not a polynomial, $\displaystyle 5x^{1.5} + 1.5x - 3$ is not a polynomial.

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

Thanks so much!
$\displaystyle \cos$ is not a polynomial so $\displaystyle \cos (5x + 1)$ is not a polynomial.

RonL

5. 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

Thanks!
Your second problem is different in nature to the first so you should repost

RonL

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

$\displaystyle (\sqrt x)^3$

Thanks

7. Originally Posted by phgao
Thanks!
can you explain why power of 1.5 is the same as what you have typed:

$\displaystyle (\sqrt x)^3$

Thanks
First we need:

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

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

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

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

Again by the law of indices:

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

RonL

8. Originally Posted by phgao
Thanks!
can you explain why power of 1.5 is the same as what you have typed:

$\displaystyle (\sqrt x)^3$

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