Divide
-20^6-24x^4-12x^2/-4x^4
Divide
-20^6-24x^4-12x^2/-4x^4
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}
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?