We have to divide 3x

^{3}- 5x

^{2}+ 10x - 3 by 3x + 1.

We use following procedure to get result,

In first step of polynomial division we just search leading ‘x’ of the divisor where leading dividend is 3x

^{3}. Now we divide the leading 3x

^{3}by 3x and we get x

^{2}as a result on the top after that we take that x

^{2}and multiply with divisor 3x+1.first we multiply x

^{2}with 3x and carry 3x

^{3}underneath then we multiply x

^{2}with 1 and carry the x

^{2}underneath now we draw the equals bar to subtract lowest term from upper term. To subtract lowest term we change sign of lowest terms.

After changing all the signs of lowest term 3x

^{3}will cancels out. -5x

^{2}and -x

^{2}both add up and as a result we get -6x

^{2}. And after that we have to remember one thing that carry has to be moved down that’s why 10x - 3 moves down from the dividend. Now again we divide the -6x

^{2}+ 10x - 3 term with divisor 3x + 1, here we search which is the leading ‘x’ term in the bottom line dividend. -6x

^{2}is the leading ‘x’ term so again after divide we get -2x at the bottom.

Again multiply divisor with -2x term so after multiply with 3x we get -6x

^{2}and with 1, we get -2x. After that both carry are underneath and same as above and signs will change. After subtracting both -6x

^{2}will cancel out and both 10x and 2x will add up. Once again we divide the bottom line dividend 12x-3 from divisor 3x + 1 and we get -7 remainder as a result.