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