Math Is Fun Forum / Adding and Subtracting Polynomials

SlowlyFading · 2012-08-09 05:25:38

These are the problems I got wrong on my newest lesson. I've tried a couple times to correct them and keep coming up with the wrong answer. If somebody could solve and show their so I can understand how to do it, that would be awesome!

The Questions I got wrong:
6. 5x2 – 3x – 7

7. 4x4 – 3x2 + 7x – 11

8. 5x6 + 6x5 – 4x3 + x2 – 45

9. 3x – 4

10. 8x5 – 7x3 + 4

For 7 - 10 it says, " identify the degree of the polynomial."

11. (9x2 + 3x – 5) + (8x2 – x + 2)

12. (4x2 – x – 5) + (6x2 + x)

For those two it says, "add or subtract the given polynomials."

THANKS!

bobbym · 2012-08-09 05:38:27

Hi;

This is a 4th degree polynomial.

Take a look here,

http://www.mathsisfun.com/algebra/degre … ssion.html

http://en.wikipedia.org/wiki/Degree_of_a_polynomial

now try 8,9, and 10 on your own. Post your answers below.

careless25 · 2012-08-09 05:45:05

Hi SlowlyFading,

The degree of the polynomial is the highest degree in the polynomial.
For example:

has 3 as the highest degree, so the degree of the polynomial is 3.

Adding and subtracting polynomials is just like adding and subtracting numbers. You collect the like terms(the terms which have the same degree) and add or subtract them together.

For example:

First you take care of the negative sign:

Then group the like terms together:

And now add or subtract:

Follow these rules and try the questions you have posted again. Post your answers here, so we can see where you went wrong.

Cheers,
C25

PS Also look at the links bobbym posted

Last edited by careless25 (2012-08-09 05:47:14)

noelevans · 2012-08-09 07:20:24

Hi SlowlyFading!
There's no reason to be slowly fading here. There is an easier way to write and work these.

are place value like in arithmetic. They can be rewritten as 8 27 -9 and 6 20 1 leaving spaces
between the coefficients since they go with different powers of x. Line them up just like in
arithmetic and add or subtract.

8 27 -9
6 20 1
_________ and get the sum and difference like in arithmetic except you have signed numbers.

14 47 -8 is the sum. ...NEVER... carry or borrow between columns because the base
is unknown so we can't tell how much we are borrowing, etc.
2 7 -10 is the difference This makes the algebra easier than the arithmetic.

Put the powers of x back in like you would powers of 10 (squared, first power, constant)

are the sum and difference, respectively.

If there are missing powers of x in the polynomial then you must put zeros for the coefficients
in the short form.

This is somewhat like asking someone to write you a check for $31 and seeing if they mind you
slipping in a couple of zeros ($3001). The zeros make a difference.

We are taught quite well to do short forms in arithmetic, but in algebra they go back to the
expanded forms. That makes in all harder: Try to multiply 497*859 in the form

writing out all the exponents of 10 throughout. How much fun would that be?

I hope this will help you and not confuse you. Consider it like the options I saw for dinner in
a restaurant: 1) Take it. 2) Leave it.

SlowlyFading · 2012-08-10 05:14:50

For 6 - 10:

6. 5x2 – 3x – 7
The degree of this one is 2

7. Was already done for me.

8. 5x6 + 6x5 – 4x3 + x2 – 45
This one is 6.

9. 3x – 4
It's 1 maybe?

10. 8x5 – 7x3 + 4
this one is 5.

Are these correct?

bobbym · 2012-08-10 05:23:46

Hi SlowlyFading;

You are now an expert on getting the order or degree of a polynomial! Very good!

Now if we can only get you to use latex...

noelevans · 2012-08-10 05:31:02

Hi slowlyfading!

They look good to me.

3x4-2x3+5x-3 is of degree 4, right? 3x^4-2x^3+5x-3 is the way these are usually typed.

And if you want them to look really nice put "math" in brackets [ ] before you type it and "/math"
in brackets afterwards.

It should look like this:

You can leftclick on the "pretty math" line and it will show you what was typed to get it.
The \\ before and after just causes the "pretty math" to be on a separate line.

SlowlyFading · 2012-08-11 03:56:32

I don't even know what latex is bobbym..

Now 11:
11. \\(9x^2 + 3x – 5) + (8x^2 – x + 2)\\

So far I have, \\8x^2 + 11x - 3\\ and \\2x^2 - 1x - 1\\

Is that correct? What's next or is it done..?

I used the method from post #4

bob bundy · 2012-08-11 04:10:26

hi SlowlyFading,

This is your algebra written in Latex:

So let's write it without the brackets:

Now I'll move together 'like terms' moving the + and - signs along with the numbers and letters.

It is important to keep the signs attached to each term!

Now simplify like terms.

and we're finished.

Bob

SlowlyFading · 2012-08-12 05:31:15

Awesome!

For;
12. (4x^2 – x – 5) + (6x^2 + x)
4x^2 - 6x^2 - 5 + x
10x^2 + 5

careless25 · 2012-08-12 06:41:48

hi,

Almost correct! It is

bob bundy · 2012-08-12 07:03:10

hi SlowlyFading

12. (4x^2 – x – 5) + (6x^2 + x)

Do one step at a time.

(i) Take away the brackets

(ii) Keep the sign with the term and move like terms together

(iii) Simplify the terms

Bob

SlowlyFading · 2012-08-13 13:51:06

Okay, thanks guys.
I have a few more similar problems from my next lesson and I'm going to post them and my answers. I would appreciate it someone check them for me and tell me where/how/what the correct answer is.

I think I'm understanding it. It seems really simple actually but I need to get used to and get a grasp on it. It's the simplifying part I don't understand how to do, I don't understand that part crystal clear yet. Oh, and the moving terms part. For example; (8x^2 – x + 2) Does the negative sign or positive sign belong to the x? I don't know things like that.. Never done this before.

careless25 · 2012-08-13 13:58:22

Hey

The negative sign does not "belong" to x, think of it as -1 * x = -1x = - x.

Does that make sense?

bobbym · 2012-08-13 14:14:59

Hi SlowlyFading;

For example; (8x^2 – x + 2)

What does that mean?

bob bundy · 2012-08-13 16:48:25

hi SlowlyFading,

The rules of algebra are the same as the rules of arithmetic, so one thing you can do, when you are unsure, is to try the same thing with numbers.

That minus sign is telling you the 'x' has got to be subtracted so that's why I say move the sign with the term.

Hope that helps.

Bob

noelevans · 2012-08-14 01:25:42

Hi everyone!

The "-" can go either way. If it is between two numbers/letters like 2x-3 then this is a subtraction
and the terms involved in the subtraction are 2x and 3. Hence the "-" does not go with the 3.

On the other hand if we apply the definition of subtraction to get 2x+(-3) then the two terms
being added are 2x and -3. Hence the "-" goes with the three.

If all the subtractions are written as additions of opposites, then the terms (including their signs)
can be moved about indiscriminantly since addition is both commutative and associative.
Hence, as Bob said you can rearrange the terms if you "keep the sign with the term."

3x - y + 7z - 6a - 2b
= 3x+(-y)+7z+(-6a)+(-2b) by applying the definition of subtraction
= 3x+7z+(-y)+(-6a)+(-2b) putting "like" terms together.
= 3x + 7z -y - 6a - 2b

Last edited by noelevans (2012-08-14 01:45:05)

SlowlyFading · 2012-08-14 05:19:30

Okay, thanks guys! I think I'm understanding this..

13. (8x^2 + 2x + 1) + (x^2 – 4x + 7)
The answer should be 9x2 – 2x + 8?

14. (7x + 4) – (2x + 9)
The answer should be 5x – 13? Or is it 9x + 13 ?

15. (4x^3 + 6x^2 – 8x) – (x3 - 2x^2 + 12x)
The answer should be 5x^6 + 4x^2 – 4x ?

16. (x3 + 2x^2 + 5x) – (3x^2 – x – 7)
The answer should be -2x^3 + x2 - 2x ?

17. (5x^4 – 2x^2) – (3x – 2x^2 - 4x^3 + 6x^4)
The answer should be 9x^4 - x3 + 4x^2 + 3x?

18. (-x^2 + 4x - 3) + (x2 – 2x + 6)
The answer should be ?

19. (-4x3 – x2 + 8) + (5x2 - x – 12)
The answer should be 9x3 – x - 4?

20. (-5x2 - 5x + 3) – (6x2 – x)
The answer should be -11x2 - 4x + 3?

bob bundy · 2012-08-14 07:31:07

hi Slowlyfading,

some right, but some not

13. (8x^2 + 2x + 1) + (x^2 – 4x + 7)
The answer should be 9x2 – 2x + 8?

correct.

14. (7x + 4) – (2x + 9)
The answer should be 5x – 13? Or is it 9x + 13 ?

7x - 2x = 5x. But not 13 at all. You should have 4 - 9 = ??

15. (4x^3 + 6x^2 – 8x) – (x3 - 2x^2 + 12x)
The answer should be 5x^6 + 4x^2 – 4x ?

x^6 ??? 6x^2 -- 2x^2 is not 4x^2 -8x - 12x is not -4x

Let's work on this one before looking at the rest.

I think you should write out all the steps each time. You are less likely to make any mistakes.

Remove the brackets. Notice the minus in the second bracket now becomes a plus.

Collect together like terms.

Simplify the like terms

16. (x3 + 2x^2 + 5x) – (3x^2 – x – 7)
The answer should be -2x^3 + x2 - 2x ?

You are muddling terms that are not'like'. Try correcting this like I have shown you.

17. (5x^4 – 2x^2) – (3x – 2x^2 - 4x^3 + 6x^4)
The answer should be 9x^4 - x3 + 4x^2 + 3x?

The same problem here. The like terms are in a different order. Try correcting this like I have shown you.

18. (-x^2 + 4x - 3) + (x2 – 2x + 6)
The answer should be ?

Try correcting this like I have shown you.

19. (-4x3 – x2 + 8) + (5x2 - x – 12)
The answer should be 9x3 – x - 4?

-x and -4 Ok but the x^3 and x^2 terms are not right. Try correcting this like I have shown you.

20. (-5x2 - 5x + 3) – (6x2 – x)
The answer should be -11x2 - 4x + 3?

correct.

Bob

noelevans · 2012-08-14 12:52:49

Hi Slowlyfading!

How are you at adding, subtracting, multiplying and dividing positive and negative numbers?
That could possibly be part of your problem. Try these: "*" means times.

1) 7-(-2) = 2) -8-3= 3) -9+5= 4) -3*(-4)= 5) -5-(-7)=

6) 7-(-3)= 7) -5+(-9)= 8) -18/3= 9) -2-7= 10) (-2)-(-9)=

One needs to be extremely accurate ( 99+%) to be able to work algebra problems that have a
number of operations in each problem. For example if one is 90% accurate, then doing 4 of the
problems like you have been doing will have 10 or so signed number operations. Missing one in
10 will make one of the four problems wrong and so a 75% correct out of the four problems.

Give these 10 problems a try to see if you are having difficulty with these operations.

SlowlyFading · 2012-08-15 02:19:32

Okay, I tried those 10 problems noelevens!

1) 7-(-2) = 9

2) -8-3= 5

3) -9+5= -4

4) -3*(-4)= 12

5) -5-(-7)= 2

6) 7-(-3)= 10

7) -5+(-9)= -14

8) -18/3= -6

9) -2-7= -9

10) (-2)-(-9)= 7

I'm pretty sure these are all correct.. I think my problem is with the rearranging the numbers so you can simplify. I don't know how to do that very well.

bobbym · 2012-08-15 02:29:56

Hi SlowlyFading;

noelevans · 2012-08-15 02:53:51

Hi SlowlyFading!

That's pretty good -- a 90%. If that's pretty much the average of the number of mistakes you
make in these basic operations, then you could probably profit greatly by practice, practice,
practice until these operations cause no concern at all.

On the other hand if it was just a "brain freeze" on that one problem and you are really near 100%
then more power to you. Subtraction seems to be the hardest operation for most people. In
algebra with signed numbers it is usually best to change it into an addition problem: Leave the first
number alone, change the "-" subtraction symbol into "+", and take the opposite of the second
number (that is change the sign of the second number). That's the definition of subtraction.

Examples: 8-(-3)=8+3=11 -4-9=-4+(-9)=-13 2-7=2+(-7)=-5 -9-(-7)=-9+7=-2

Part of the reason people have trouble with this is that we are expected to do it all in our heads.
This means we have to mentally change to an addition problem and then do that in our heads.
Addition is easier than subtraction since in addition problems we don't have to change to a
different problem before working it.

SlowlyFading · 2012-08-16 03:33:52

Thanks noelevens!

Okay, Bob Bundy, I've redone the first 2 I got wrong. Hopefully, this is better.

14. (7x + 4) – (2x + 9)
5x – 5

16. (x3 + 2x^2 + 5x) – (3x^2 – x – 7)
x3 – x2 + 6x + 7

17. (5x^4 – 2x^2) – (3x – 2x^2 - 4x^3 + 6x^4)
-2x^4 - x3 + 4x^2 + 3x

18. (-x^2 + 4x - 3) + (x2 – 2x + 6)
2x^2 + 2x + 3

19. (-4x^3 – x2 + 8) + (5x^2 - x – 12)
-4x^3 + 4x^2 – x + 4

noelevans · 2012-08-16 05:39:39

Hi SlowlyFading! 14 and 16 were correct. The others just slightly off.

I have trouble following the input to LaTex (You can see it if you click on the "pretty math" output).
It's much easier to see what's going on in the pretty output. Maybe that is part of the problem if
you are looking at the ^ notation as you are trying to work the problem. Writing it by hand
like the pretty LaTex output might be easier to work with.

It's really easy to do the LaTex input for these. You are ALREADY typing the correct input lines.
You just need to put (math) before and (/math) after BUT use [...] instead of (...). All the \\ does
is create a new line. LaTex does the correct spacing in its output automatically, so the spaces that
you insert into the input don't really count. Use spaces there to make it look better to you.
Compare your line to the first line below it by looking at your line and then left clicking on the next
line. You will see that they are essentially the same except for the = and \\'s causing new lines.

To do this LaTex you need to do the "Post a reply" not the "Quick post." That way you have the
opportunity to click the "preview" button to see how it is going.

17. (5x^4 – 2x^2) – (3x – 2x^2 - 4x^3 + 6x^4)

18. (-x^2 + 4x - 3) + (x2 – 2x + 6)

19. (-4x^3 – x2 + 8) + (5x^2 - x – 12)

You'll notice that in going from the first "pretty" line to the second "pretty" line that I started with
the highest power available and scanned both polynomials for the terms with that power and then
put both of them next to each other (if there were some in both polynomials).

HANG IN THERE!!! You are well on the way.

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#1 2012-08-09 05:25:38

Adding and Subtracting Polynomials

#2 2012-08-09 05:38:27

Re: Adding and Subtracting Polynomials

#3 2012-08-09 05:45:05

Re: Adding and Subtracting Polynomials

#4 2012-08-09 07:20:24

Re: Adding and Subtracting Polynomials

#5 2012-08-10 05:14:50

Re: Adding and Subtracting Polynomials

#6 2012-08-10 05:23:46

Re: Adding and Subtracting Polynomials

#7 2012-08-10 05:31:02

Re: Adding and Subtracting Polynomials

#8 2012-08-11 03:56:32

Re: Adding and Subtracting Polynomials

#9 2012-08-11 04:10:26

Re: Adding and Subtracting Polynomials

#10 2012-08-12 05:31:15

Re: Adding and Subtracting Polynomials

#11 2012-08-12 06:41:48

Re: Adding and Subtracting Polynomials

#12 2012-08-12 07:03:10

Re: Adding and Subtracting Polynomials

#13 2012-08-13 13:51:06

Re: Adding and Subtracting Polynomials

#14 2012-08-13 13:58:22

Re: Adding and Subtracting Polynomials

#15 2012-08-13 14:14:59

Re: Adding and Subtracting Polynomials

#16 2012-08-13 16:48:25

Re: Adding and Subtracting Polynomials

#17 2012-08-14 01:25:42

Re: Adding and Subtracting Polynomials

#18 2012-08-14 05:19:30

Re: Adding and Subtracting Polynomials

#19 2012-08-14 07:31:07

Re: Adding and Subtracting Polynomials

#20 2012-08-14 12:52:49

Re: Adding and Subtracting Polynomials

#21 2012-08-15 02:19:32

Re: Adding and Subtracting Polynomials

#22 2012-08-15 02:29:56

Re: Adding and Subtracting Polynomials

#23 2012-08-15 02:53:51

Re: Adding and Subtracting Polynomials

#24 2012-08-16 03:33:52

Re: Adding and Subtracting Polynomials

#25 2012-08-16 05:39:39

Re: Adding and Subtracting Polynomials

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