Question

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Answer 1

Answer:

whats the answer fo q(x)

Step-by-step explanation:

Answer 2

Answer:

The given expression can be written in the form $q(x)+\frac{r(x)}{b(x)}$ as $(2x^2-x+3)+\frac{0}{x-3}$ where  q(x)=$2x^2-x+3$ , r(x)=0 and b(x)=x-3

Step-by-step explanation:

Given rational expression is $\frac{2x^3-7x^2+6x-9}{x-3}$

To rewrite the given rational expression in the given form  and match their correct expressions:

Rewrite the given rational expression $\frac{2x^3-7x^2+6x-9}{x-3}$ in the form of $q(x)+\frac{r(x)}{b(x)}$ 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 $2x^3-7x^2+6x-9$

Therefore b(x)=x-3

3_|   2     -7     6     -9

       0      6    -3      9

   ------------------------------------

      2      -1       3      0

  ------------------------------------

Therefore we have quadratic equation $2x^2-x+3=0$

q(x)=$2x^2-x+3$

Remainder is 0

Therefore r(x)=0

Therefore we can write in the form as $(2x^2-x+3)+\frac{0}{x-3}$

It is in the form of $q(x)+\frac{r(x)}{b(x)}$

Therefore the given expression can be written in the form $q(x)+\frac{r(x)}{b(x)}$ as $(2x^2-x+3)+\frac{0}{x-3}$ where  q(x)=$2x^2-x+3$ , r(x)=0 and b(x)=x-3