Forgot how to Factor

Well, even though you're in Calculus, it's okay that you've momentarily forgotten how to factor. Brain farts happen to the best of us. My first step here would be to find a common factor and pull it out. You have three terms there. Do they have any common factors? For instance, do they all contain an x? Are they all divisible by some number? Once you do that, you should have two terms multiplied together, one of which is a standard quadratic of the form:

x^2 + bx + c = (x+?)(x+?)

Now remember back to the rules for factoring you learned so long ago back in Algebra class. You want to find two numbers which multiply to c and add up to b. Can you do that? It might help if you list all the factors of c​.
 
How do you factor (-16x^2 + 96x) - 80
The parentheses aren't necessary; the quadratic is -16x2 + 96x - 80.

The first step is the simple factoring you learned back in pre-algebra or beginning algebra. (here) First, pull the common factor of -16 out front. Remember to be careful of the signs. (here and here)

To learn how to factor the quadratic (which they should have covered in algebra or pre-calc), try here.

Once you have studied the lessons at the links, please attempt the exercise. If you get stuck, please reply showing your efforts so far, so we can help you move forward. Thank you! ;)
 
How do you factor (-16x^2 + 96x) - 80

You've received some good advice already but sometimes I just can't see what's in front of my face so I do it a different way. If a quadratic is factor-able you can find (some of) the factors by using the quadratic equation. As an example take
16 x2 + 16 x - 32 = 0
If we use the quadratic equation we find that the roots are 1 and -2, so we know 2 factors and we can write
16 x2 + 16 x - 32 = a (x-1) (x+2)
Since 16 is the coefficient of x2 on the left, it must also be so on the the right and a=16 for the third factor. Thus
16 x2 + 16 x - 32 = 16 (x-1) (x+2)
which was probably pretty easy to see this time. But it won't always be so.
 
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