Question

Rewrite the rational expression( x^3-7x^2+13x-3) / (x-3) in the form q(x) +

Answer 1

Answer:

$q(x)=x^2-4x+1$

$b(x)=x-3$

$r(x)=0$

Step-by-step explanation:

The given rational expression is

$\dfrac{x^3-7x^2+13x-3}{x-3}$

We need to write this expression as

$q(x)+\dfrac{r(x)}{b(x)}$

where, q(x) is quotient, r(x) is remainder and b(x) is divisor.

$b(x)=x-3$

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.

$q(x)=x^2-4x+1$

$r(x)=0$

The given expression can be written as

$x^2-4x+1+\dfrac{0}{x-3}$

Answer 2

The correct answers are:
q(x) = $x^2-4x+1$
b(x) = x-3
r(x) = 0

Explanation:
By using synthetic division, we would get:
   | 1   -7    13  -3
3 |      3   -12   3
---------------------------------
     1   -4      1   0

q(x) = [1 -4 1] = $1*x^2-4x+1$
b(x) = x - 3 (Expression with which you're dividing)
r(x) = 0 (Since the last reminder is 0)