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:
`(10 x^(6) )/(5 x^(2) ) + (20 x^(4) )/(5 x^(2) ) - (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`