Questions: (a) q(x)=(x+3)^4-3(x+3)^2 (b) r(x)=x^4-3x^2-2 (c) s(x)=x^4/256-3x^2/16

Solution Steps

(a) To find the function $q(x)$, we need to expand and simplify the expression $(x+3)^4 - 3(x+3)^2$.

(b) The function $r(x)$ is already simplified, so we can directly evaluate it for any given $x$.

(c) The function $s(x)$ is also already simplified, so we can directly evaluate it for any given $x$.

We start with the function $q(x) = (x + 3)^4 - 3(x + 3)^2$. By expanding and simplifying, we find: $$q(x) = (x + 3)^2 \left( (x + 3)^2 - 3 \right)$$ Thus, the simplified form of $q(x)$ is: $$q(x) = (x + 3)^2 \left( x^2 + 6x + 6 \right)$$

The function $r(x)$ is given as: $$r(x) = x^4 - 3x^2 - 2$$ This expression is already in its simplest form.

The function $s(x)$ is given as: $$s(x) = \frac{x^4}{256} - \frac{3x^2}{16}$$ This expression is also in its simplest form.

Final Answer