Question

what is f(x)/g(x) when f(x) = 6x3 – 19x2 + 16x – 4 and g(x) = x - 2? 6x^2 - 7x + 2 3x² - 9x + 8 6x2 – 7x + 2 - 8/(x - 2) 3x2 - 9x + 8 - 8/(x - 2)

Answer 1

Problem

what is f(x)/g(x) when f(x) = 6x3 – 19x2 + 16x – 4 and g(x) = x - 2?

Solution

We can use the long division and we have:

$\frac{6x^3-19x^2+16x-4}{x-2}=6x^2+\frac{-7x^2+16x-4}{x-2}$

We can simplify the last expression on this way:

$6x^2+\frac{-7x^2+16x-2}{x-2}=6x^2-7x+\frac{2x-4}{x-2}=6x^2-7x+2$

And the best solution for this case would be:

6x^2 - 7x + 2