Question

Given that f(x) = x^2 - 19x + 90 and g(x) = x - 10, find (f divided by g)(x) and express the result in standard form.

(a) (f divided by g)(x) = x + 9
(b) (f divided by g)(x) = x - 9
(c) (f divided by g)(x) = x + 10
(d) (f divided by g)(x) = x - 10

Answer 1

By performing polynomial long division or synthetic division, we find that (f divided by g)(x) = x - 9.

Step-by-step explanation:

To find (f divided by g)(x), we need to divide the function f(x) by g(x). Given that f(x) = x² - 19x + 90 and g(x) = x - 10, we can perform polynomial long division or synthetic division to find the quotient.

Let's perform the division:

Divide the first term of f(x) by the first term of g(x), which is x.

Multiply the entire divisor by x to get x² - 10x and subtract this from f(x).

Bring down the next term of f(x), which will give us a new dividend of -9x + 90.

Repeat the process: divide -9x by x to get -9, multiply the entire divisor by -9, which gives us -9x + 90, and subtract from the new dividend.

This leaves us with a remainder of 0, indicating that g(x) is indeed a factor of f(x).

Therefore, (f divided by g)(x) = x - 9, which is option (b).