Set up the problem like traditional long division. Divide the first term of the dividend by the first term of the divisor. #4x^3# divided by #x#, gives #4x^2#. Place #4x^2# over the squared term of the dividend. Then multiply #4x^2# by the divisor. Place the result, #4x^3 +8x^2#, under the dividend, lining up the cubed and squared terms.
Next. subtract #4x^3 +8x^2# from the dividend. Be careful to subtract the #8x^2# term from #3x^2#. Draw a line underneath, and write the result, #-5x^2#. Then "pull down" the next term from the dividend, giving you #-5x^2 -3x# under the line.
Divide the first term of the "new dividend" (#-5x^2-3x#) by the first term of the divisor (#x-2#). #(-5x^2)/x =-5x#. Place this result over the "x term" of the dividend. Multiply this result by the divisor and write it underneath. So #-5x * (x-2) = -5x^2-10x#, and #-5x^2-10x# is the next line of the problem. Subtract from the line above. Be careful. You are subtracting #-3x -(-10x)#.
Draw a line again, and write the answer, #7x# underneath. Pull down the last term, 14. Divide #7x# by x and write the answer #7# over the constant term of the dividend. Multiply and subtract like in the previous steps. You should get zero.
See the picture. Lots of words for a simple problem illustrated below.
