Question

Divide the following polynomials and then complete the quotient. Write your answer in order of decreasing powers of x.

(10x^6 + 20x^4 - 15x^2) ÷ 5x^2 = x^4 + x -

Answer 1

The easiest way to do this is to put each term in the numerator over the denominator and do the division/reducing for each one.  Like this: $\frac{10 x^{6} }{5 x^{2} } + \frac{20 x^{4} }{5 x^{2} } - \frac{15 x^{2} }{5 x^{2} }$.  The first term reduces to $2 x^{4}$, the second to $4 x^{2}$, and the third to 3.  Putting them all together with the signs in between we have $2 x^{4} +4 x^{2} -3$