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

1 Answer
Ken C.
Sep 28, 2015

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.

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