Verified answer

Pick some divisor, say, (2x - 5)

Multiply the divisor by the quotient, then add the remainder:

(x+3) (2x - 5) + 2

Do the multiplication and addition:

2x^2 + x - 13

So the requested polynomial division is:

(2x^2 + x - 13) / (2x - 5) = (x + 3) with remainder 2

Choose your own divisor and figure your own dividend. If you want to get fancy you could make the divisor a quadratic, a cubic or even higher degree polynomial.

x^3 + 2x^2 - x - 2 only take x^2 elementary from the 1st 2 words, and take -a million elementary from the final 2 words = x^2(x + 2) - a million(x + 2) you are able to now take (x + 2) elementary = (x + 2)(x^2 - a million) and in case you extra desire to factorize, you comprehend that x^2 - a million = (x + a million)(x - a million), so = (x + 2)(x + a million)(x - a million) use polynomial branch to locate (x^3 - 6x^2 + 6x - 2) / (x - a million) first placed it in branch form x - a million ) x^3 - 6x^2 + 6x - 2 first multiply by skill of x^2 to get an x^3, which you will cancel out with the x^3 on the astounding x - a million ) x^3 - 6x^2 + 6x - 2 ( x^2 x^3 - x^2 ------------- (subtract, which skill opposite the signs and warning signs) - 5x^2 + 6x (and produce down the 6x) next multiply by skill of -5x to cancel out the -5x^2 the -5x is extra to the acceptable end of the quotient, as completed under: x - a million ) x^3 - 6x^2 + 6x - 2 ( x^2 - 5x x^3 - x^2 ------------- - 5x^2 + 6x - 5x^2 + 5x ---------------- (subtract lower back) x - 2 (and produce down the -2) now ultimately you are able to only multiply by skill of a million to cancel out the x x - a million ) x^3 - 6x^2 + 6x - 2 ( x^2 - 5x + a million x^3 - x^2 ------------- - 5x^2 + 6x - 5x^2 + 5x ---------------- x - 2 x - a million ------- -a million there you have it: (x³ - 6x² + 6x -2) ÷ (x – a million) supplies: quotient: x^2 - 5x + a million the rest: -a million