SOLUTION: divide using long division (3x^3-11x^2-56x-43) divided by (3x+4) i don't understand how to do this

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Question 836299: divide using long division
(3x^3-11x^2-56x-43) divided by (3x+4)


i don't understand how to do this

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
If you UNDERSTAND long division of decimal or whole numbers, then polynomial division is really exactly the same. Instead of place value in powers of 10, you have x. You have powers of x instead of powers of 10.

This is easier to show either on paper, or interactively, if you have some capability for this; some online system maybe?


3x+4________|_____1x^2_____-(14/3)x_____(112/9)____________________________
____________|_____3x^3_____-11x^2_______-56x_______-43
____________|
____________|____3x^3______4x^2
____________|___________________
____________|_____0________-14x^2 ....._-56x
____________|______________-14x^2_______-(56/3)x
____________|____________________________________
____________|_______________0___________(112/3)x.....-43
____________|___________________________(112/3)x_____448/9
____________|_______________________________________________
____________|_____________________________0_________(-835/9), the remainder

The quotient is highlight%28x%5E2-%2814%2F3%29x%2B%28112%2F9%29-%28835%2F9%29%281%2F%283x%2B4%29%29%29
which can be a bit more simplified for the remainder and the mixed numbers if you wanted.