Question

Is 3 - x the same as x + 3 (since you rearrange the terms?)?

Answer 1

Oops, x - 3

Answer 2

3 - x is not the same as x - 3
Because in the first one, the x is negative and the 3 is positive and in the second one, the x is positive and the 3 is negative.

Answer 3

now...3 - x is the same as -x + 3

Answer 4

Thanks!

Answer 5

no problem :)

Answer 6

In order for two polynomials to be equal, all terms of one polynomial must equal all corresponding terms of the other polynomial.
A polynomial of more than one term is a SUM of terms.

Subtraction can be written as the sum of the opposite.
For example, 5 - 3 is the same as 5 + (-3).
Similarly, x - 6 can be written as x + (-6) which is now a sum.

Let's look at both of your polynomials and write them as sums of terms.

First polynomial: 3 - x
3 - x = 3 + (-x)
In descending order of degree, then
3 - x = 3 + (-x) = -x + 3

Second polynomial: x - 3
x - 3 = x + (-3)

The terms of the first polynomial are -x and 3.
The terms of the second polynomial are x and -3.

Since in general x≠−x and since \(3 \ne -3\), the corresponding terms are not equal, and the polynomials are not equal.

Notice what the polynomials are, though. They are opposites, or additive inverses, since they add to zero.
(3 - x ) + (x - 3 ) = 3 - x + x - 3 = 3 - 3 - x + x = 0