Question

Rewrite the rational expression in the form , and then match q(x), r(x), and b(x) to the correct expressions.

x^3-7x^2+13x-3/x-3

TILES ;
x^2-7x+13
x^3-7x^2+13x-3
-3
x^2-4x+1
x-3
0

PAIRS ;

q(x)
b(x)
r(x)

Answer 1

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

b(x) = x - 3

r(x) = 0

Explanation:

plato

Answer 2

First step do the division.
However, before diving in the division, check that there is no remainder by substituting (x-3)=0, or x=3 into the numerator. If the result is 0, there is no remainder.
f(x)=x^3-7*x^2+13*x-3, and f(3)=27-63+39-3=0 so no remainder.
We can proceed with the long division to get
(x^3-7*x^2+13*x-3)/(x-3)=x^2-4x+1
So choose the factors (x^2-4x+1) and (x-3) and choose the appropriate function.

Note: question is not very complete with details, it seems that the question had been abridged.
Advice: post the complete and unabridged question if *correct* answers are exprected *rapidly*.