Respuesta :
Answer:
The given expression can be written in the form [tex]q(x)+\frac{r(x)}{b(x)}[/tex] as [tex](2x^2-x+3)+\frac{0}{x-3}[/tex] where q(x)=[tex]2x^2-x+3[/tex] , r(x)=0 and b(x)=x-3
Step-by-step explanation:
Given rational expression is [tex]\frac{2x^3-7x^2+6x-9}{x-3}[/tex]
To rewrite the given rational expression in the given form and match their correct expressions:
Rewrite the given rational expression [tex]\frac{2x^3-7x^2+6x-9}{x-3}[/tex] in the form of [tex]q(x)+\frac{r(x)}{b(x)}[/tex] where q(x) is the quotient, r(x) is the remainder and b(x) is the divisor.
Now solve the given expression by using Synthetic division, we get
Since x-3 is a factor for [tex]2x^3-7x^2+6x-9[/tex]
Therefore b(x)=x-3
3_| 2 -7 6 -9
0 6 -3 9
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2 -1 3 0
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Therefore we have quadratic equation [tex]2x^2-x+3=0[/tex]
q(x)=[tex]2x^2-x+3[/tex]
Remainder is 0
Therefore r(x)=0
Therefore we can write in the form as [tex](2x^2-x+3)+\frac{0}{x-3}[/tex]
It is in the form of [tex]q(x)+\frac{r(x)}{b(x)}[/tex]
