Let f(x) = −8x2 − 5x and g(x) = 17x2 + 11x. find f(x) − g(x).

So what we're doing is subtracting g(x) from f(x). If f(x) = -8x^2 - 5x, and g(x) = 17x^2 + 11x, we're just subtracting two binomials.

(- 8x^2 - 5x) - (17x^2 + 11x) Is our problem. If you don't know how to subtract polynomials, I'll show you step by step.

First you want to distribute the implied ones to get rid of the parenthesis. This means that you multiply the first set of numbers by 1, and the second by -1. The first set will stay the same, but when you multiply the second set by -1, both terms will become negative.

(- 8x^2 - 5x) - (17x^2 + 11x)
1(- 8x^2 - 5x) - 1(17x^2 + 11x)
-8x^2 - 5x - 17x^2 - 11x.

Now, we want to add/subtract like terms. Like terms are terms with the same variable and exponent. All we do is add/subtract the coefficient. The variable and exponent will stay the same. If a term does not a show a coefficient, then the coefficient is 1.

-8x^2 and -17x^2 are like terms. Subtract the coefficients.
-8 - 17 = -25
-8x^2 - 17x^2 = -25x^2

-5x - 11x
-5 - 11 = -6
-5x - 11x = -6x

So our final result is -25x^2 - 6x.

Hope this helps!!
Let me know if you need help understanding anything and I'll try to explain as best I can.