Answer:
[tex]q(x)=x^{3} -8x+2[/tex]
[tex]r(x)= \frac{3}{x}[/tex]
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 [tex]x^{2} +x[/tex]. If I were to divide [tex]x^{2} +x[/tex] by x, my answer would be (x+1) since x(x+1) equals [tex]x^{2} +x[/tex].
Now lets divide [tex]x^{3} -8x^{2} +2x+3[/tex] by x. I start by dividing x into the first term.
[tex]\frac{x^{3} }{x} =x^{2}[/tex] because x times [tex]x^{2}[/tex] is [tex]x^{3}[/tex].
Next we divide x into the second term.
[tex]\frac{-8x^{2} }{x} = -8x[/tex].
We continue by dividing x into the third term.
[tex]\frac{2x}{x} =2[/tex]
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 [tex]\frac{3}{x}[/tex].
We put together all the quotients we found by dividing each term and get [tex]q(x)=x^{3} -8x+2[/tex].
