Question

Please help with khan

Answer 1

Answer:

$q(x)=x^{3} -8x+2$

$r(x)= \frac{3}{x}$

Step-by-step 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.

$\frac{x^{3} }{x} =x^{2}$ because x times $x^{2}$ is $x^{3}$.

Next we divide x into the second term.

$\frac{-8x^{2} }{x} = -8x$.

We continue by dividing x into the third term.

$\frac{2x}{x} =2$

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 $\frac{3}{x}$.

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