SOLUTION: Please help me with this problem i am doing an online class and am stuck on this particualar question. I simply do not know what i am suppose to do. Please help. The question says

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me with this problem i am doing an online class and am stuck on this particualar question. I simply do not know what i am suppose to do. Please help. The question says       Log On


   

Question 88881: Please help me with this problem i am doing an online class and am stuck on this particualar question. I simply do not know what i am suppose to do. Please help. The question says you must "Divide by using long division" here is the question +%28x%5E3%2B6x%5E2-x-30%29+divided+by+%28x-2%29+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E3%2B6x%5E2-x-30%29%2F%28x-2%29 Start with the given expression



This expression also looks like


x-2
x%5E3%2B6x%5E2-x-30


In order to divide this, we need to ask ourselves:
How many times does x go into x%5E3+?
It goes in x%5E2 times (ie x%5E3+%2Fx=x%5E2). So place x%5E2 over x%5E3+

x%5E2
x-2
x%5E3%2B6x%5E2-x-30

Now multiply x%5E2 by x+-+2 to get x%5E3+-+2x%5E2
x%5E2
x-2
x%5E3%2B6x%5E2-x-30
x%5E3+-+2x%5E2

Now Subtract x%5E3+-+2x%5E2 from x%5E3%2B6x%5E2-x-30 and bring down -x-30
x%5E2
x-2
x%5E3%2B6x%5E2-x-30
x%5E3+-+2x%5E2
......8x%5E2+-+x+-+30


Now how many times does x go into 8x%5E2?
It goes in 8x times (ie 8x%5E2+%2Fx+=8x). So place 8x over 6x%5E2

x%5E2%2B8x
x-2
x%5E3%2B6x%5E2-x-30
x%5E3+-+2x%5E2
......8x%5E2+-+x+-+30

Now multiply 8x by x+-+2 to get 8x%5E2+-+16x
x%5E2%2B8x
x-2
x%5E3%2B6x%5E2-x-30
x%5E3+-+2x%5E2
......8x%5E2+-+x+-+30
......8x%5E2+-+16x

Now Subtract 8x%5E2+-+16x from 8x%5E2+-+x+-+30
x%5E2%2B8x
x-2
x%5E3%2B6x%5E2-x-30
x%5E3+-+2x%5E2
......8x%5E2+-+x+-+30
......8x%5E2+-+16x
............15x+-+30


Now how many times does x go into 15x?
It goes in 15 times (ie 15x+%2Fx+=15). So place 15 over -x

x%5E2%2B8x%2B15
x-2
x%5E3%2B6x%5E2-x-30
x%5E3+-+2x%5E2
......8x%5E2+-+x+-+30
......8x%5E2+-+16x
............15x+-+30

Now multiply 15 by x+-+2 to get 15x+-+30
x%5E2%2B8x%2B15
x-2
x%5E3%2B6x%5E2-x-30
x%5E3+-+2x%5E2
......8x%5E2+-+x+-+30
......8x%5E2+-+16x
............15x+-+30
............15x+-+30

Now Subtract 15x+-+30 from 15x+-+30
x%5E2%2B8x%2B15
x-2
x%5E3%2B6x%5E2-x-30
x%5E3+-+2x%5E2
......8x%5E2+-+x+-+30
......8x%5E2+-+16x
............15x+-+30
............15x+-+30
..................%280%29


So we get a remainder of zero. This means x-2 is a factor of x%5E3%2B6x%5E2-x-30