How do you write the polynomial 3x^2-8x- 12x^5- 5x3+ 2x^4- 63x2−8x−12x5−5x3+2x4−6 in standard form?

1 Answer
Shell
Dec 4, 2016

-12x^5+2x^4-5x^3+3x^2-8x-6−12x5+2x4−5x3+3x2−8x−6

Explanation:

I am assuming the 33 in the -5x−5x term should be an exponent.

3x^2-8x-12x^5-5x^3+2x^4-63x2−8x−12x5−5x3+2x4−6

To write the polynomial in standard form, write it in order of decreasing exponents. I have highlighted the exponents in red.

-12x^color(red)5+2x^color(red)4-5x^color(red)3+3x^color(red)2-8x-6−12x5+2x4−5x3+3x2−8x−6

Note that the 8x8x term has an exponent of color(red)11 (8x^color(red)18x1), but the color(red)11 is not typically written.

And, even the -6−6 term has an exponent. Recall that x^0=1x0=1, so -6=-6x^color(red)0−6=−6x0. So the constant term -6−6 also follows the rule of writing the terms in order of decreasing exponents.

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