Answer:
[tex]q(x)=x^2-4x+1[/tex]
[tex]b(x)=x-3[/tex]
[tex]r(x)=0[/tex]
Step-by-step explanation:
The given rational expression is
[tex]\dfrac{x^3-7x^2+13x-3}{x-3}[/tex]
We need to write this expression as
[tex]q(x)+\dfrac{r(x)}{b(x)}[/tex]
where, q(x) is quotient, r(x) is remainder and b(x) is divisor.
[tex]b(x)=x-3[/tex]
The coefficients of dividend are 1, -7, 13 and -3.
Using synthetic division, we get
3 | 1 -7 13 -3
| 3 -12 3
------------------------------------
1 -4 1 0
------------------------------------
First three elements of bottom row represents the quotient and last element of bottom row represents the remainder.
[tex]q(x)=x^2-4x+1[/tex]
[tex]r(x)=0[/tex]
The given expression can be written as
[tex]x^2-4x+1+\dfrac{0}{x-3}[/tex]
