I am supposed to divide (x^3+6x^2-20) by x^2+2, using long division. I know it's very difficult to type long division on the computer, but if you would be able to give me the answer, and I'd work backwords, that would be great, or a simple explanation.

http://www.sosmath.com/algebra/factor/fac01/fac01.html

Certainly! Long division can be a bit challenging to explain without visual representation, but I'll try my best to explain the process step by step.

To divide (x^3+6x^2-20) by (x^2+2) using long division, you would go through the following steps:

Step 1: Divide the first term of the dividend (x^3) by the first term of the divisor (x^2) to obtain the first term of the quotient. In this case, x^3 divided by x^2 equals x. Write the result (x) as the first term of the quotient.

Step 2: Multiply the entire divisor (x^2+2) by the first term of the quotient (x). In this case, x multiplied by (x^2+2) equals x^3+2x. Write this result (x^3+2x) below the dividend, aligned with the corresponding terms.

x
____________________
x^2+2 | x^3 + 6x^2 - 20
x^3 + 2x
_________________
4x^2 - 20

Step 3: Subtract the result obtained in Step 2 from the dividend. In this case, subtract (x^3+2x) from (x^3+6x^2-20). The subtraction yields 4x^2-20. Write this as the new dividend.

Step 4: Bring down the next term of the dividend (in this case, -20) as the new last term of the new dividend.

Step 5: Divide the first term of the new dividend (4x^2) by the first term of the divisor (x^2) to obtain the next term of the quotient. In this case, 4x^2 divided by x^2 equals 4. Write the result (4) as the next term of the quotient.

Step 6: Multiply the entire divisor (x^2+2) by the next term of the quotient (4). In this case, 4 multiplied by (x^2+2) equals 4x^2+8. Write this result (4x^2+8) below the new dividend, aligned with the corresponding terms.

x + 4
____________________
x^2+2 | x^3 + 6x^2 - 20
x^3 + 2x
_________________
4x^2 - 20
4x^2 + 8
______________
-28

Step 7: Subtract the result obtained in Step 6 from the new dividend. In this case, subtract (4x^2+8) from (4x^2-20). The subtraction yields -28.

Step 8: Since there are no more terms left in the dividend, the long division process is complete.

The final quotient is x + 4, and the remainder is -28.

So, (x^3+6x^2-20) divided by (x^2+2) equals (x + 4) with a remainder of -28.

I hope this explanation helps!