Exercise 3 Page 964

We are given two functions and we want to find the difference between them.

f (x) = x^{3} - 4 x^{2} + 9 x - 12 g (x) = 6 x^{3} + x^{2} - 5 x - 12

Let's substitute the given function rules for

f (x)

and

g (x) .

f (x) - g (x)

$f (x) = x^{3} - 4 x^{2} + 9 x$ , $g (x) = 6 x^{3} + x^{2} - 5 x - 12$

(x^{3} - 4 x^{2} + 9 x) - (6 x^{3} + x^{2} - 5 x - 12)

Now that we have done the substitutions, we are able to perform the subtraction. Let's start by using the Distributive Property.

(x^{3} - 4 x^{2} + 9 x) - (6 x^{3} + x^{2} - 5 x - 12)

Remove parentheses

x^{3} - 4 x^{2} + 9 x - (6 x^{3} + x^{2} - 5 x - 12)

Distribute $- 1$

x^{3} - 4 x^{2} + 9 x - 6 x^{3} - x^{2} + 5 x + 12

Add and subtract terms

- 5 x^{3} - 5 x^{2} + 14 x + 12

This corresponds to option A.