G(x) = 35x^2– 48x – 27; 7x + 3
how do i solve this using long division?

35x² = 7x • 5x, and

5x (7x + 3) = 35x² + 15x

Subtract this from the dividend to get an initial remainder of

(35x² - 48x - 27) - (35x² + 15x) = -63x - 27

-63x = 7x • (-9), and

-9 (7x + 3) = -63x - 27

Subtract this from the previous remainder to get a new one of

(-63x - 27) - (-63x - 27) = 0

and we're done.

Now just gather the terms in bold (and the remainder, but since it's 0 we leave it out). So we have

(35x² - 48x - 27) / (7x + 3) = 5x - (63x + 27) / (7x + 3)

(35x² - 48x - 27) / (7x + 3) = 5x - 9