### Instruction: For what values of $x$ is $x^2-2x>35$? Express your answer in interval notation.### Response: I notice that this is a quadratic inequality, so I want to rewrite it in standard form by subtracting 35 from both sides.
This gives me $x^2-2x-35>0$.
Now I want to factor the left-hand side to find the critical points where the sign of the expression changes.
I look for two numbers that multiply to -35 and add to -2, and I find that -7 and 5 work.
So I can factor the left-hand side as $(x-7)(x+5)>0$.
This means that the expression is positive when both factors are positive or both are negative.
This happens when $x>7$ or $x<-5$.
So the solution set is the union of these two intervals, which I can write in interval notation as $(-\infty,-5)\cup(7,\infty)$.