Divide

-20^6-24x^4-12x^2/-4x^4

Divide

-20^6-24x^4-12x^2/-4x^4

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There is more then one way to do this problem. Since the denominator is a monomial (only one term), I would first separate the problem like this:(-20x^6/-4x^4)+(-24x^4/-4x^4)+(-12x^2/-4x^4)

Next, I would divide within each set of parentheses.

For the first set, -20/-4 = 5, and x^6/x^4 = x^2 (when the same variable is in the numerator and the denominator, you subtract the exponents). So the first set becomes 5x^2

For the second set, -24/-4 = 6, and x^4/x^4 = 1 (subtracting 4-4 = 0, and x^0 = 1, since anything^0 = 1). So we get 6 * 1 = 6

For the last set, -12/-4 = 3, and x^2/x^4 =x^-2. Negative exponents are not permitted in a completely simplified answer, so a term with a negative exponent still needs work. x^-2 is the same as 1/x^2 (negative exponents get "flipped"- moved from numerator to denominator or denominator to numerator, and then become positive). So we get 3* 1/x^2 = 3/x^2

Final answer is 5x^2 + 6 + 3/x^2

I can't be sure what form the answer is expected to have.

You could divide the numerator and denominator by -4x^{2}:

-20x^{6} - 24x^{4} - 12x^{2} 5x^{4} + 6x^{2} + 3

----------------------- = ---------------

-4x^{4} x^{2}

Or you could do this:

-20x^{6} - 24x^{4} - 12x^{2}^{ }-20x^{6} -24x^{4} -12x^{2} 3

----------------------- = ------- + ------ + ------ = 5x^{2} + 6 + ---

-4x^{4} -4x^{4} -4x^{4} -4x^{4} x^{2}

Amaan M.

Former High School Math and Economics Teacher

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Gregory R.

Graduate student teaching Violin, Viola, Music Theory, and Composition

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## Comments

I have a question, Amy. Pardon me, if it's a dumb question. Why is that negative exponents are not permitted in a completely simplified answer?? Is there a rule of math I missed that says something about it?