Question

If r (x) = x3 - x2 + x and s (x) = -x, which expression is equivalent to (r/s) (x)?----

a) X³+x².
b) -x²+x-1.
c) X²-x+1.
d) X²-x

Answer 1

The expression equivalent to (r/s)(x) is -x^2 + x - 1.

Step-by-step explanation:

To find the expression equivalent to (r/s)(x), we need to divide the polynomial r(x) by s(x). First, let's divide each term of r(x) by -x:

r(x) = (x^3 - x^2 + x) / -x

Dividing each term by -x gives us:

r(x) = -x^2 + x - 1

Therefore, the expression equivalent to (r/s)(x) is -x^2 + x - 1, which is option b) in the given choices.