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demha

Member

Registered: 2012-11-25

Posts: 195

Multiplying and Dividing Polynomials

I am having a hard time understanding how to do these correctly. Could someone please help explain how to do them step by step?

1. (3x + 6x)/3x

2. (21x3 + 14x) / 7

3. (4x5 + 8x2) / 4x

4. [2(x – 1) + 3(x – 1)] / (x – 1)

5. [3(2x – 3) – x(2x – 3)] / (2x - 3)

6. [x2(5x + 6) – 3(5x + 6)] / (5x + 6)

7. [3x2(2x - 3) + 27x3(2x - 3)] / [3x(3 – 2x)]

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Bob

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Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

hi demha

OK let's start with Q1

Now you could simplify the top first but, looking at the later ones, it is probably better to split into two fractions.

Can you finish this one from here?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

Sorry I haven't answered sooner. I have been busy with other matters.

To finish from there. If I'm correct, we have to reduce it.
So:

3x/3x + 6x/3x

Reducing:
1x/1x + 3x/1x

For first fraction:
1x goes into 1x one time so it will become just x.

For second fraction:
1x goes into 3x three times so it will become 3x.

So the problem becomes x + 3x. So the answer is 4x?

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"The thing about quotes on the Internet is you cannot confirm their validity"
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Agnishom

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Re: Multiplying and Dividing Polynomials

For first fraction:
1x goes into 1x one time so it will become just x.

No it will become 1

Similarly, 6x/3x = 2

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demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

So you don't reduce them?

So then:
3x/3x + 6x/3x

For first fraction:
3x goes into 3x 1 time.

For second fraction:
3x goes into 6x 2 times.

Then it becomes 1 + 2 and of course the answer is 3.

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

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Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

hi demha

That's correct.  Shall we try Q2 ?

Try to split this one into two fractions and then simplfy each one.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

So that would be set as:

21x^3/7 + 14x/7

For the first fraction:
7 goes into 21x 3x times I suppose. This will leave it with 3x^3?

For the second fraction:
7 goes into 14x 2x times.

The problem then becomes:

3x^3 + 2x

They are not entirely alike so you can't add them. Therefor that is the answer I believe?

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

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Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

hi demha,

Yes, that's correct, well done.

The others are similar, although the expressions get more complicated.

How about trying Q3 and Q4 and then I'll check them.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

3.
(4x^5 + 8x^2) / 4x

4x^5/4x + 8x^2/4x

For first equation:
4x goes into 4x 1 time so it will be 1^5

For second equation:
4x goes into 8x 2 times so it will be 2^2.

It will then be:
1^5 + 2^2

I hope I did this one correct.

Number 4 seems to be pretty complicated. I'm not too sure how to start it!

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

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Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

hi demha,

You shouldn't have lost the xs.  Have a look at this:

Cancel the 4 top and bottom and one x top and bottom to leave

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

Oh alright! And the: 8x^2/4x would become 2x?

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Multiplying and Dividing Polynomials

That is correct!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

So how would you do number 4?

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

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Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

hi demha

Q4.  Same method:

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

2(x – 1) + 3(x – 1) / (x – 1)

2(x – 1)/(x - 1) + 3(x – 1)/( x - 1)

For the first fraction:
so (x - 1) goes into (x - 1) one time making it 2(1). Now I want to stop right here and make sure that I'm doing this right.

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

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Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

yes.  first part is 2.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

Glad to know I'm on the right track.
Second part of the equation:
3(x – 1)/( x - 1)

Same way, (x - 1) goes into (x - 1) 1 time making it 3(1).

So now the equation is:
2 + 3 and the final answer will be 5.

Am I correct?

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Multiplying and Dividing Polynomials

Hi;

Correct! Very good!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

Well done.

5, 6 and 7 are very similar to 4, so have a go and post your answers.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

#5
[3(2x – 3) – x(2x – 3)] / (2x - 3)

First fraction:
3(2x - 3)/(2x - 3)
(2x - 3) goes into (2x - 3) 1 time.
3(1)

Second fraction:
x(2x - 3)/(2x - 3)
(2x - 3) goes into (2x - 3) 1 time.
x(1)

Answer:
3 - x

#6
[x2(5x + 6) – 3(5x + 6)] / (5x + 6)

First fraction:
x^2(5x + 6)/(5x + 6)
(5x + 6) goes into (5x + 6) 1 time.
x^2(1)

Second fraction:
3(5x + 6)/(5x + 6)
(5x + 6) goes into (5x + 6) 1 time.
3(1)

x^2 - 3

#7
[3x^2(2x - 3) + 27x^3(2x - 3)] / [3x(3 – 2x)]

This one seems a little confusing.

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I also have two more having some trouble with:

8. 15x^7 – 45x^5 / 3x4

19. (3x – 2)(x - 4) – (x - 4)(6 – 5x) / (4 – x)(8x – 1)

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

#5
[3(2x – 3) – x(2x – 3)] / (2x - 3)

First fraction:
3(2x - 3)/(2x - 3)
(2x - 3) goes into (2x - 3) 1 time.
3(1)

Second fraction:
x(2x - 3)/(2x - 3)
(2x - 3) goes into (2x - 3) 1 time.
x(1)

Answer:
3 - x
correct!
#6
[x2(5x + 6) – 3(5x + 6)] / (5x + 6)

First fraction:
x^2(5x + 6)/(5x + 6)
(5x + 6) goes into (5x + 6) 1 time.
x^2(1)

Second fraction:
3(5x + 6)/(5x + 6)
(5x + 6) goes into (5x + 6) 1 time.
3(1)

x^2 - 3
correct!
#7
[3x^2(2x - 3) + 27x^3(2x - 3)] / [3x(3 – 2x)]

This one seems a little confusing.

At this stage you can divide each part and then simplify. 

(3-2x) goes into (2x-3) exactly minus 1 times

Let's get this one finished and then we can look at 8 and 9. 

Bob

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I also have two more having some trouble with:

8. 15x^7 – 45x^5 / 3x4

19. (3x – 2)(x - 4) – (x - 4)(6 – 5x) / (4 – x)(8x – 1)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

[3x^2(2x - 3) + 27x^3(2x - 3)] / [3x(3 – 2x)]

First one:
3x^2(2x - 3)/3x(3 – 2x)]

So since it is (2x - 3) and (3 - 2x), it goies into it but it becomes a -1? And as for the 3x^2 and 3x, would this becomes x^2?

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

Wait, I think it just becomes x(-1)

27x^3(2x - 3) / 3x(3 – 2x)

(2x - 3) goes into (3 - 2x) -1 time. 3x goes into 27 9 times and takes down the ^3 to ^2 which makes it 9^2(-1)

-x + -9^2

Is that correct?

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Multiplying and Dividing Polynomials

Nearly

takes down the ^3 to ^2 which makes it 9^2(-1)

should be 9x^2(-1)

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

demha

Member

Registered: 2012-11-25

Posts: 195

Re: Multiplying and Dividing Polynomials

So the equation is

-x + -9x^2 then?

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"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln