Question 965643
______________|_______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:   {{{(2x-7)(5x-4)=10x^2-43x+28}}}.