Expert: Chanda Walker - 4/30/2009

Question
QUESTION: Hi, Ms. Walker. I'm having trouble with a few questions, and appreciate some clarification.

Simplify, arrange the terms in order of decreasing degree of x and find the degree of the polynomial for:

2x^3 - 7 + 5x^2 - x^3 + 3x - x^3

Simplifying I get 5x^2+3x-7, but I don't know what "arrange the terms in order of decreasing degree of x and find the degree of the polynomial" exactly means. Especially finding the degree.

Find an equation of the form f(x) = mx + b:

f(0) = 5 and f(2) = 7

I don't even know where to start with the above question.

This question is so simple, but I simply have forgotten whether to add or multiple to simplify :

Simplify (assume the variable represents positive integers):  (-t^3)4

Also, do you know what exactly is meant by " (assume the variable represents positive integers) "

Here a few question I just need checked :

Simplify: (x^2^n - y^n)^2
My answer : x^4^n - y^2^n

Simplify (assume the variable exponents represent positive integers): x^2(x^k - x^k^-1 + x^k^-2)
My answer : x^2^k - x^2^k^-2 + x^2^k^-4

I'm honestly kind of lost, and mostly unsure of myself. Your help is appreciated. I haven't been able to get in contact with my teacher in awhile.

ANSWER: Simplify, arrange the terms in order of decreasing degree of x and find the degree of the polynomial for:

2x^3 - 7 + 5x^2 - x^3 + 3x - x^3

Simplifying I get 5x^2+3x-7, but I don't know what "arrange the terms in order of decreasing degree of x and find the degree of the polynomial" exactly means. Especially finding the degree.


You've done this perfectly.  Putting the x^2 term first, then the x term, and finally the number last is arranging them in order of decreasing degree.  And the degree is the highest exponent on x.  So it is a second degree equation since the highest exponent is 2.

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Find an equation of the form f(x) = mx + b:

f(0) = 5 and f(2) = 7

I don't even know where to start with the above question.

This question is so simple, but I simply have forgotten whether to add or multiple to simplify :

Start by using substitution.

f(0) = 5  is the information to substitute.  It would look like this:

f(0) = m (0) + b = 5
therefore
b = 5

Now put that into the next substitution:

f(2) = m (2) + 5 = 7
2m + 5 = 7
2m = 2
m = 1

Your function is:
f(x) = x + 5

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Simplify (assume the variable represents positive integers):  (-t^3)4

Also, do you know what exactly is meant by " (assume the variable represents positive integers) "

t is never smaller than 1 and is always an integer so you can see that the term inside the parenthesis is always negative.  The question I don't know is whether that 4 is intended to be an exponent.  If it is this is the answer:

t^12

If it is not this is the answer:
=-4t^3

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Simplify: (x^2^n - y^n)^2
My answer : x^4^n - y^2^n

I'm not sure if you equations are supposed to be:

(x^2)^n or x^(2^n)

Looking at how you typed out the answer you gave, I think it is the first way.

If it is the first way:
x^4n - 2x^4n y^2n + y^2n

If it is the second way:
x^(4^n) - 2 (x^(2^n))(y^n) + y^2n


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Simplify (assume the variable exponents represent positive integers): x^2(x^k - x^k^-1 + x^k^-2)
My answer : x^2^k - x^2^k^-2 + x^2^k^-4

Again I have confusion about how the problem is intended to be asked:
The first way would yield:

x^2k - x^(2-k) + x^(2-2k)



I really don't think the second way is the right so I won't bother putting the answer.  It gets really messy.

---------- FOLLOW-UP ----------

QUESTION: You're right it is suppose to be  (-t^3)^4. Eeek.

On the second to last one, I didn't know how to show the two variables right next to each other were both exponents, beside putting " ^ " before each. I see that you used parenthesis.

Second to last should be " (x(^2n)-y^n)^2. I had did the same for the last. It should be : x^2(x^k-x(^k-1)+x(^k-2))

Extra help, please? :) I have two of these question " Find the GCF and LCM for the monomials: " If shown how to do the first i'd be able to do the other

22xy^2z^2, 33x^2yz^2, 44x^2yz

Answer
Formatting in pure text is a real bear.  The first answers I gave should be accurate for the first problem but that second one is still a little squirrelly.

Is the exponent of the second term in the parenthesis is:
k-1 or is it -k?

Here is the answer if it is k-1,

x^(2+k) - x(k+1) + x^k

If it is -k then the answer I gave previously almost applies.  I just noticed a mistake.  Sorry!

x^(2+k) - x^(2-k) + x^(2 - 2k)

Again my apologies.

The rule is that when you multiply terms with the same base (here it is x) you add their exponents.  If you have a term with an exponent to the exponent, you multiply.

Here are some easier examples.

x^2  * x^3 = x*x   * x*x*x  = x^5 (the 2 and the 3 summed to 5)

If you have (x^2)^3 = (x*x)*(x*x)*(x*x) = x^6 (the 2 and the 3 multiplied)

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I think they just want you to find the greatest common factor and the least common multiple (or sometimes called the lowest common multiple) for all three monomials at the same time.  It doesn't make sense to me to factor a single monomial.  If you have any information that may enlighten me to what factoring a monomial might mean, share it with me and I'll try to help you again.

But with that being said, I'll answer this the best I know how.

GCF = 11xyz

You can factor that out of each monomial.

LCM = (11* 2*3*4)x^2y^2z^2
= 264 x^2 y^2 z^2

Let me know if I can help further.