Question

Please help with khan

Answer 1

`q(x)=x^(3) -8x+2`

`r(x)= (3)/(x)`

Explanation:

When dividing numbers, we find the quotient or answer by knowing multiplication facts. When 9 is divided by 3, we know that 3x3=9. This 3 is our answer.

When dividing polynomials, we find the quotient by knowing how to multiply expressions. For instance, x(x+1) can be found by multiplying (using the distributive property) x by x to get x squared and then multiplying x by 1 to get x. This gives the expression
`x^(2) +x`. If I were to divide
`x^(2) +x` by x, my answer would be (x+1) since x(x+1) equals
`x^(2) +x`.

Now lets divide
`x^(3) -8x^(2) +2x+3` by x. I start by dividing x into the first term.

`(x^(3) )/(x) =x^(2)` because x times
`x^(2)` is
`x^(3)`.

Next we divide x into the second term.

`(-8x^(2) )/(x) = -8x`.

We continue by dividing x into the third term.

`(2x)/(x) =2`

We finish by dividing x into the last term. But because 3 has no variable this can not be done. Nothing times x will give just 3. So r(x) or our remainder will be
`(3)/(x)`.

We put together all the quotients we found by dividing each term and get
`q(x)=x^(3) -8x+2`.