Problem
For the following pair of functions, find $2[Q(x)]-R(x)$. \[ Q(x)=3 x^{2}-9 x+5 \text { and } R(x)=12 x^{2}-2 \] $2[Q(x)]-R(x)=$ (Simplify your answer. Do not factor.)
Solution
Step 1 ：Find 2 times Q(x): $2(3x^2 - 9x + 5) = 6x^2 - 18x + 10$
Step 2 ：Subtract R(x) from the result: $(6x^2 - 18x + 10) - (12x^2 - 2) = -6x^2 - 18x + 12$
Step 3 ：\boxed{-6x^2 - 18x + 12}
