So I just started college this week after a break from school and we had a problem where we needed to find f(x)=2x^2-x+3 when f(x) is f(a-4). We've already gotten the answer, but one of the first steps they did to solve it was make 2(a-4)^2 into 2(a^2-8a+16). How/what did they do to get to this? I remember learning this in high school but, like I said, I haven't been to school in a while so I don't remember how to do it. If someone could give me a step by step demonstration or a resource to go learn it myself, that'd be great!
Answers (3)
A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.
Now study this page until it seems obvious: en.wikipedia.org/wiki/Polynomial_remainder_theorem