Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

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!

I'm just here to get some help with an online math course I'm taking.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**careless25****Real Member**- Registered: 2008-07-24
- Posts: 559

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 (2012-08-08 07:47:14)*

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Offline

**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

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?

I'm just here to get some help with an online math course I'm taking.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Offline

**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

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

I'm just here to get some help with an online math course I'm taking.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,706

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

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

Offline

**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

Awesome!

For;

12. (4x^2 x 5) + (6x^2 + x)

4x^2 - 6x^2 - 5 + x

10x^2 + 5

I'm just here to get some help with an online math course I'm taking.

Offline

**careless25****Real Member**- Registered: 2008-07-24
- Posts: 559

hi,

Almost correct! It is

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,706

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

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

Offline

**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

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.

I'm just here to get some help with an online math course I'm taking.

Offline

**careless25****Real Member**- Registered: 2008-07-24
- Posts: 559

Hey

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

Does that make sense?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

Hi SlowlyFading;

For example; (8x^2 x + 2)

What does that mean?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,706

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

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

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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 (2012-08-13 03:45:05)*

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Offline

**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

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?

I'm just here to get some help with an online math course I'm taking.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,706

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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.

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Offline

**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

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.

I'm just here to get some help with an online math course I'm taking.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

Hi SlowlyFading;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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.

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Offline

**SlowlyFading****Member**- Registered: 2012-06-12
- Posts: 149

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

I'm just here to get some help with an online math course I'm taking.

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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.

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Offline