# Thread: I am Requesting to Have Someone Check my Work on Polynomials

1. ## I am Requesting to Have Someone Check my Work on Polynomials

Below is a set of six questions that were included in my assignment. I think I have a pretty good understanding but I am not real sure I am doing the long division ones the right way. If someone could check my work and provide feedback for anything that I am not doing correctly, I would really appreciate it. Thank you in advance for your time.

1. Give examples for a Real number and a Complex number.

Real numbers
natural numbers (1, 2, 3, 4, 5, etc.)
whole numbers (0, 1, 2, 3, 4, etc.)
integers (…-5, -4, -3, -2, -1, 0, 1, 2, etc.)
decimal numbers (0.1, 0.2, 0.3, 0.4, etc.)
rational numbers (7/4, 50/100, ½, etc.)
irrational numbers (1/3, 10/11, 3/13, 22/7 or 3.14, etc.)

Complex numbers
5i
22i
17i
5i
4i
9i
3i

2. Simplify the following expressions

(a). (x3)2

X6

(b). y5.y8

y13

(c). (x3y5)/y2

x3y3

(d). 27a^4b^8c^-3
----------------
3a^-3b^2

9a^7b^6
---------
c3

(e). (x+4)(x+6)

x2 + 10x + 24

(f). (x2-3)(x +7)

x3 + 7x2 – 3x – 21

3. Simplify (x2 +8x +15)/(x2-25)

4. Simplify a^3 + 9a^2 + 27a + 27
----------------------
a + 3

(a + 3)(a + 3)(a + 3)
--------------------
a + 3

5. Divide x^4 + 3x^3 + x^2 + 1 by (x-1)

6. Divide 6y^3 + 2 by (y + 1)

2. I got to 2c before I got a headache. I'd be happy to check the rest if you use Latex.

Also, note that e.g. 5i+9 also is a complex number. Generally, a complex number can be described as a+bi with a and b being real numbers.

3. Hi Pim,

Thank you for responding...sorry about the headache. I will redo them using Latex and will post back.

4. You "irrational numbers" are all wrong- they are in fact just rational numbers. Examples of irrational numbers are such things as $\displaystyle \sqrt{3}$, $\displaystyle \sqrt[3]{4}$, $\displaystyle \pi$, and e. Did the problem actually ask for examples of natural numbers, whole numbers, etc.? The heading only says "real numbers" and "complex numbers". Your examples of complex numbers happen to all be imaginary numbers. You should include examples like "3+ 2i", etc. In fact, since the real numbers are a subset of the complex numbers, it would, technically, be correct to include "0", "1", and "1/3", say, as examples of complex numbers- but your teacher might not accept that.

I presume that by "(x3)2" you really mean $\displaystyle (x^3)^2$ (double click on that to see the LaTex code. If you don't want to use LaTex, at least us "^" to indicate a power). Yes, that is $\displaystyle x^6$. Assuming that, for the other like that, a number following a letter means a power, yes, those are correct.

For (4) it would be better to write $\displaystyle \frac{x^3+ 9x^2+ 27x+ 27}{x+ 3}= x^2+ 6x+ 9$ or $\displaystyle (x+ 3)^2$ rather than leave it as a fraction.

(5) and (6) are correct though, since both divisors are of the form "x- a", "synthetic division" might be simpler.

5. Thank you HallsofIvy for the response, I apologize for not making sure the problems were written correctly. I noted the suggestions for question 1 and have made corrections as shown below. In addition, I corrected question 4 and removed it along with questions 5 & 6 as they were correct.

1. Give examples for a (i) Real number (ii) Complex number

Real numbers

2 + 5
-5 + 20
0.25 - 0.30
1/3

Complex numbers

22i - 7i
17i + 2
5i - 1
(3+2i) + (1+3i)

2. Simplify the following expressions

(a) $\displaystyle (x^3)^2$

$\displaystyle x^6$

(b) $\displaystyle y^5.y^8$

$\displaystyle y^1^3$

(c) $\displaystyle (x^3y^5)/y^2$

$\displaystyle x^3y^3$

(d) $\displaystyle 27a^4b^8c^-^3 / 3a^-^3b^2$

$\displaystyle 9a^7b^6/c^3$

(e) $\displaystyle (x+4)(x+6)$

$\displaystyle x^2 + 10x + 24$

(f) $\displaystyle (x^2-3)(x +7)$

$\displaystyle x^3 + 7x^2 – 3x – 21$

3. Simplify $\displaystyle (x^2 + 8x +15)/(x^2-25)$

6. Originally Posted by dclary
Complex numbers

22i - 7i
17i + 2
5i - 1
(3+2i) + (1+3i)
Complex numbers are in the form of a + bi. So you might as well write your complex numbers like these:
15i
2 + 17i
-1 + 5i
4 + 5i

Originally Posted by dclary
3. Simplify $\displaystyle (x^2 + 8x +15)/(x^2-25)$

Long division isn't really needed here. I think it would actually be better to simplify by factoring the numerator & denominator, like this:
\displaystyle \begin{aligned} \dfrac{x^2 + 8x +15}{x^2-25} &= \dfrac{(x + 3)(x + 5)}{(x - 5)(x + 5)} \\ &= \dfrac{x + 3}{x - 5} \end{aligned}

7. Hello emuyang,

Thank you for the response, you have been very helpful. I am assuming that question 2, letters a - f, were correct?

8. I wasn't looking at #2a-f. But they look okay, although the LaTeX in 2f is screwy on my computer for some reason. Let me test:
$\displaystyle x^3 + 7x^2 – 3x – 21$
$\displaystyle x^3 + 7x^2 - 3x - 21$
I see; it's the minus signs. Can't use the longer minus sign in LaTeX, looks like.

9. Great, thank you again. After looking back, it did the same for me, I will have to watch that in the future...Latex appears to be very sensitive. Thank you again.