can you explain long division step by step with words. i always forget what to do....?

Question

1) 8x^3+x^2-x+6 divided by x+1

Answer 1

D,M,S,B
daddy, mother, sister, brother
divide, multiply, subtract, bringdown

8x^3 divided by x is 8x^2
8x^2 * (x+1) is 8x^3 + 8x^2
subtract this from 8x^3 + x^2 you get -7x^2
bring down -x
divide -7x^2by x and get -7x
multiply -7x *(x+1) and get -7x^2-7x
subtract this from -7x^2-x and get 6x
bring down +6 and you have 6x+6
divide 6x by x and get 6
multiply 6*(x+1) and get 6x+6
subtract this from 6x+6 and get 0 which means no remainder
the answer is 8x^2 - 7x + 6

Answer 2

Set it up this way:

x + 1)8x^3 + x^2 - x + 6

8x^3/x = 8x^2:
Enter 8x^2 above the 8x^3 term
. . . . 8x^2
x + 1)8x^3 + x^2 - x + 6
Multiply x + 1 by 8x^2 and enter the result beneath:
. . . . 8x^2
x + 1)8x^3 + . x^2 - x + 6
. . . . 8x^3 + 8x^2
Subtract:
. . . . 8x^2
x + 1)8x^3 + . x^2 - x + 6
. . . - 8x^3 -. 8x^2
. . . . . . . . . - 7x^2 - x + 6
Divide by x again, adding the result to the quotient:
. . . . 8x^2 - 7x
x + 1)8x^3 + . x^2 - x + 6
. . . - 8x^3 -. 8x^2
. . . . . . . . . - 7x^2 - x + 6
Multiply x + 1 by -7x:
. . . . 8x^2 - 7x
x + 1)8x^3 + . x^2 - x + 6
. . . - 8x^3 -. 8x^2
. . . . . . . . . - 7x^2 - x + 6
. . . . . . . . . - 7x^2 - 7x
Subtract again:
. . . . 8x^2 - 7x
x + 1)8x^3 + . x^2 - x + 6
. . . - 8x^3 -. 8x^2
. . . . . . . . . - 7x^2 .. - x + 6
. . . . . . . .. + 7x^2 + 7x
. . . . . . . . . . . . . . . . 6x + 6
Divide again:
. . . . 8x^2 - 7x + 6
x + 1)8x^3 + . x^2 - x + 6
. . . - 8x^3 -. 8x^2
. . . . . . . . . - 7x^2 .. - x + 6
. . . . . . . .. + 7x^2 + 7x
. . . . . . . . . . . . . . . . 6x + 6
Multiply x + 1 by 6:
. . . . 8x^2 - 7x + 6
x + 1)8x^3 + . x^2 - x + 6
. . . - 8x^3 -. 8x^2
. . . . . . . . . - 7x^2 .. - x + 6
. . . . . . . .. + 7x^2 + 7x
. . . . . . . . . . . . . . . . 6x + 6
. . . . . . . . . . . . . . . . 6x + 6
Subtraction will now yield 0, so there is no remainder, and the quotient is
8x^2 - 7x + 6

Check by multiplying (x + 1)(8x^2 - 7x + 6) to arrive back at 8x^3 + x^2 - x + 6

Answer 3

Divide, multiply, subract, check, bring down