Math help... If you have Teaching Textbooks Algebra 2 or understand my question

[Based on Faith Academy]

I have to understand why things are the way they are in a problem.

I am stumped as to the why this problem and subsequent problems are 

the way they are.

 

Solve and give every solution:

 

They are third degree problems. An example would be x(cubed)minus 3x(squared)minus 6x plus eight equals zero.

-2 is a solution.

 

My failure to understand lies in the division part of the problem. What doesn't make sense to me is how is it that I

can change the subtractions to additions and change the signs and get a completely different answer than if I just

left the subtraction as subtraction and went with the knowledge that a subtraction automatically changes the sign

to the opposite.

 

Am I making sense? TIA

[regentrude]

Solve and give every solution:

 

They are third degree problems. An example would be x(cubed)minus 3x(squared)minus 6x plus eight equals zero.

-2 is a solution.

 

My failure to understand lies in the division part of the problem. What doesn't make sense to me is how is it that I

can change the subtractions to additions and change the signs and get a completely different answer than if I just

left the subtraction as subtraction and went with the knowledge that a subtraction automatically changes the sign

to the opposite.

Am I making sense? TIA

 

No, you're not making sense to me. Here is how to do the polynomial division:

Write out the problem:

x^3-3x^2-6x+8=0. Guess x=-2 is solution.

Divide by (x-(2)) :

x^3-3x^2-6x+8 / (x+2)= ?

we know leading term of ? must be x^2, so, multiply (x+2) by x^2:

x^3+2x^2

This must be subtracted from original polynomial, just like regular long division.

Are the signs in the next step where the confusion arises?

x^3-3x^2-6x+8

- (x^3+2x^2)

= - 5x^2-6x+8   (*)

now we see next term of ? has to be - 5x

multiply (x+2) by 5x:

- 5x^2 -10x

this must be subtracted from remaining polynomial (*)

- 5x^2-6x+8  (*)

- (- 5x^2 -10x)

= 4x+8

so last term of ? has to be 4

(x+2)*4=4x+8, when this is subtracted there remains no rest.

Thus,

x^3-3x^2-6x+8 / (x+2)= x^2 - 5x +4

 

Tell me where exactly you have the problem, so I can help.

 

 

[Based on Faith Academy]

This must be subtracted from original polynomial, just like regular long division.

Are the signs in the next step where the confusion arises?

x^3-3x^2-6x+8

- (x^3+2x^2)

= - 5x^2-6x+8   (*)

 

This is the start of what makes no sense of why it is so.

In TT they changed the subtraction signs in the original problem

to addition and made the problem read....x^3+-3x^2+-6x+8.

If you add doing the problem that way you get what you got BUT

if you leave the signs as subtraction then you would get -x^2- 6x+8.

This makes no sense to me. Whether you change the sign at the start

of the problem or as you go through the problem, you should still get the

same answers(to my way of thinking) :huh:

 

[regentrude]

This is the start of what makes no sense of why it is so.

In TT they changed the subtraction signs in the original problem

to addition and made the problem read....x^3+-3x^2+-6x+8.

If you add doing the problem that way you get what you got BUT

if you leave the signs as subtraction then you would get -x^2- 6x+8.

This makes no sense to me. Whether you change the sign at the start

of the problem or as you go through the problem, you should still get the

same answers(to my way of thinking) :huh:

 

 

x^3+-3x^2+-6x+8.

is exactly the same  as

x^3 -3x^2 - 6x+8.

 

There is absolutely no difference between the two expressions, so no, I do not understand what you are saying.

 

You have to subtract :

.x^3+-3x^2+-6x+8.

- (x^3+2x^2)

The x^3 terms cancel

- 3x^2 - 2x^2 = -5x^2, irrespective of whether you write an extra "+" in front of the -3x^2

 

[Based on Faith Academy]

x^3+-3x^2+-6x+8.

is exactly the same  as

x^3 -3x^2 - 6x+8.

 

There is absolutely no difference between the two expressions, so no, I do not understand what you are saying.

 

Exactly!!

 

You have to subtract :

.x^3+-3x^2+-6x+8.OK but if you wrote it as x^3-3x^2-6x+8 then....

- (x^3+2x^2)This is my problem.. When you subtract  x^3-2x^2....

The x^3 terms cancel

- 3x^2 - 2x^2 = -5x^2, irrespective of whether you write an extra "+" in front of the -3x^2...Then -3x^2-(-2x^2)=(-x^2)??

                                                                                                                                                   Shouldn't the -2x^2 change to positive?

 

[kiana]

You shouldn't be subtracting (x^3 - 2x^2). You should be subtracting (x^3 + 2x^2). Why do you feel the sign on the 2 should change?

 

Sometimes people are taught to add the negative instead -- so they would be adding (-x^3 - 2x^2) -- this is mathematically legitimate even though I don't care for it because I feel it confuses people more. Have you gotten this mixed up with the subtracting somehow?

[letsplaymath]

Are you trying to divide by (x - 2) instead of (x + 2)? That was a typo up above, I think. If x = -2 is a solution, then the factor you need to divide out is x - (-2), which means x+2.

 

That's because if x = -2 is a solution, then the function has to = 0 when x is -2. And that means the function must have a factor that would turn into zero at that point. The factor that becomes zero when x = -2 is (x + 2), since -2 + 2 = 0.

 

[Based on Faith Academy]

Are you trying to divide by (x - 2) instead of (x + 2)? That was a typo up above, I think. If x = -2 is a solution, then the factor you need to divide out is x - (-2), which means x+2.

 

That's because if x = -2 is a solution, then the function has to = 0 when x is -2. And that means the function must have a factor that would turn into zero at that point. The factor that becomes zero when x = -2 is (x + 2), since -2 + 2 = 0.

 

 

After you divide into x^3 you get x^2 and multiply x^2 by x + 2.

From the way you showed the problem, you put an addition sign

between x^3 + 2x^2. I thought we had to bring down the subtraction

sign that was in the problem(x^3-3x^2). If I brought down the subtraction sign

then the answer would have been different then if I put an addition sign in.

Is my thinking wrong here?

 

 

[kiana]

After you divide into x^3 you get x^2 and multiply x^2 by x + 2.

From the way you showed the problem, you put an addition sign

between x^3 + 2x^2. I thought we had to bring down the subtraction

sign that was in the problem(x^3-3x^2). If I brought down the subtraction sign

then the answer would have been different then if I put an addition sign in.

Is my thinking wrong here?

 

Yes.

 

You are not bringing down the subtraction sign from the original problem. You're subtracting off the result of x^2 (x + 2).

 

If your original problem began with x^3 + 3x^2 your x^2 term would be (3x^2 - 2x^2).

[Based on Faith Academy]

I've got it!!! My problem was that I was focused on the problem and not on the signs

of the divisor when I multiplied. That was what was determining whether the problem had a subtraction or

addition between x^3 and 2x^2.Thank you so much for all your help!!!! I kept looking at

it and finally realized the answer was right there all along.