step description number 1 divide (7x) into (28x^3) to get (4x^2) because (7x) * (4x^2) = (28x^3) 2 multiply (7x+3) by (4x^2) to get (28x^3 + 12x^2) 3 subtract (28x^3 + 12x^2) from (28x^3 - 44x^2) to get (-56x^2) 4 bring down -59x from original dividend to get (-56x^2 - 59x) 5 divide (7x) into (-56x^2) to get (-8x) because (-8x) * (7x) = (-56x^2) 6 multiply (7x+3) by (-8x) to get (-56x^2 - 24x) 6 subtract (-56x^2 - 24x) from (-56x^2 - 59x) to get (-35x) 7 bring down -15 from original dividend to get (-35x - 15) 8 divide (7x) into (-35x) to get -5 because (-5) * (7x) = (-35x) 8 multiply (7x+3) by (-5) to get (-35x - 15) 9 subtract (-35x - 15) from (-35x - 15) to get 0 your answer is (4x^2 - 8x - 5) confirm by multiplying (7x+3) * (4x^2 - 8x -5) to get (28x^3 - 44x^2 - 59x - 15) See the manual calculations below:
A word of caution.
If the dividend is missing a level, then you need to insert a 0 times that level to make sure you are subtracting correctly.
example:
(7x-3) into 5x^5 - x^2 + x
rewrite your dividend as:
5x^5 + 0x^4 + 0x^3 - x^2 + x
This way when you being down the next level you are operating correctly.
also make sure the dividend and the divisor are in the standard order with the higher exponent level to the left of the lower exponent level.