SOLUTION: find the quotient and remainder using long division: 10x^2-43x+28 / 2x-7

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Question 965643: find the quotient and remainder using long division: 10x^2-43x+28 / 2x-7
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
______________|_______5x_______________________________
______________|______________________________________
2x-7__________|______10x^2_______-43x___________28
______________|_______________________________________
______________|_____


10x^2/(2x)=5x, first part of quotient. Then multiply 5x(2x-7)
and subtract....


______________|_______5x_______________________________
______________|______________________________________
2x-7__________|______10x^2_______-43x___________28
______________|_______________________________________
______________|_____10x^2________-35x
___________________________________________
______________________0_________-8x



Bring down the next figure or term, being the "28".
______________|_______5x_______________________________
______________|______________________________________
2x-7__________|______10x^2_______-43x___________28
______________|_______________________________________
______________|_____10x^2________-35x
___________________________________________
______________________0_________-8x____________28


What is -8x/(2x)?
This is -4.

______________|_______5x__________-4_____________________
______________|______________________________________
2x-7__________|______10x^2_______-43x___________28
______________|_______________________________________
______________|_____10x^2________-35x
___________________________________________
______________________0_________-8x____________28


What is -4(2x-7)? Put this result in the partial dividend, and subtract...

______________|_______5x__________-4_____________________
______________|______________________________________
2x-7__________|______10x^2_______-43x___________28
______________|_______________________________________
______________|_____10x^2________-35x
___________________________________________
______________________0_________-8x____________28
________________________________-8x____________28
_____________________________|____0____________0

The top line shows the finished quotient, and the bottom line shows any remainder, which here, is 0.
2x-7 IS a factor of the original dividend.

Meaning: %282x-7%29%285x-4%29=10x%5E2-43x%2B28.