In algorithms, we use the Big$-$O notation to abstract away unnecessary

details about the runtime of an algorithm.

Here is the big$-$O definition $($may be useful for other exercises too$)$:

Let n $>0($usually n is the size of the input$)$ and let f$($n$)$ and g$($n$)$ be two

monotone and non$-$negative functions. We say that f$($n$)=$ O$($g$($n$))$ if there

exists a constant c and a constant n$0$ such that: f$($n$)<=$ cg$($n$),$n $>$ n$0.$

The exercise asks you to use the definition to prove the following:

$$ Let f$($n$)=100$n$^2+10$n $+1000.$ The f$($n$)=$ O$($n$^2)$