Let x = -6 in

First some background on squaring negative numbers:

If you have a negative number to the second power, it is always a positive. However, the symbols required to write what I just said would be

The confusion some students have is when you see

That is not the same thing. The exponent only applies to what it is right beside.

In the case of

the only thing that gets squared is the 6 so we have a negative and then 6 times 6 or -36.

In the case of

the exponent is beside the parentheses. That tells you to multiply negative 6 times itself twice...-6 times -6, which gives you positive 36 because a negative times a negative is a positive.

Now, when you substitute values into those polynomials, if you have

you square whatever x is. If x is a negative number, when you square it, you get a positive. When I teach this, I usually have students go through the problem and replace all the variables with parentheses to help keep them from making this mistake.

For example:
Let x = -6 in

would become

Then put the -6 into the parentheses to get

Now use order of operations which says do first to get positive 36

36-8(-6)-9

Then we do 8 times -6 which is -48, but there is a minus in front of the 8 so we have
36 - -48 - 9

Using the rules for subtraction, we change the subtractions to adding the opposite to get

36 + +48 + -9   or just 36 + 48 - 9 which gives a final answer of 75.