Question

How do you write `3x^4+2x^3-5-x^4` in standard form?

Answer 1

`2x^4+2x^3-5`

Explanation:

The standard form of a polynomial (which is what we have here) is written from highest exponent to lowest exponent. In addition, there should only be 1 of each exponent/variable pair (like x^4 or x^3). For example, here we have `3x^4` and `-x^4`; but we can only have 1 term with an `x^4` in it. To fix this, we need to combine these terms by adding `3x^4` to `-x^4`; the result is `2x^4` (remember that `3x^4+(-x^4)` is the same thing as `3x^4-x^4`).

From here, we just need to organize a bit - from highest exponent to lowest. Our highest is, of course, `4`. Then we have `3` - and since we don't have `x^2` or `x`, we ignore them. Now, what about the `-5`? Well, since `x^0 = 1`, we can write `-5` as `-5x^0`, which is the same thing as `-5*1` - which equals `-5`. That makes 0 our lowest exponent. Cool, huh?

Finally, we simply write it. We start with the term with the highest exponent (`2x^4`), and then go down from there. So, our polynomial in standard form is `2x^4+2x^3-5`. And we're done.