Answer:
The quotient is [tex]10x+16[/tex]
The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]
Step-by-step explanation:
(See my image for my work)
Once the problem is set up, we need to figure out how to make [tex]x^3[/tex] become [tex]10x^4[/tex]. To do this, we must multiply it by [tex]10x[/tex].
This becomes the first number at the top of our work.
Now, we need to create the second row. To do this, we need to multiply all of the terms on the left by [tex]10x[/tex] and then multiply it by a negative.
Once that is done, we need to subtract these two rows.
After we subtract, we are left with [tex]16x^3-20x^2+26x-10[/tex]
Now we can do the same thing. This time, the number that we must multiply by is 16, so that is the next term on top
Next, we multiply the terms on the left by 16 and then subtract them from the previous expression
This leaves us with [tex]34x^2+10x+22[/tex].
As this has a smaller power than the left-hand side, this is our remainder, which we need to divide by the left hand side.
Our quotient is the number that we have found on the top.
This gives us the answer of
The quotient is [tex]10x+16[/tex]
The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]
(Sorry. This process is hard to do in this form, so I had to write it by hand.)
