Help - How do you find the values of m for the equation "(m+2)x^2-2mx+1=0"?

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.

(m + 2)x^2 - 2mx + 1 = 0 Add spaces to improve readability. Then apply the pattern.

(ax + b)(cx + d) = acx^2 + (ad + bc)x + bd

ac = m + 2
ad + bc = -2m
bd = 1 Since we assume integer answers, this implies b = d = 1. So rewrite accordingly.

a + c = -2m
ac = m + 2 Now apply the usual methods to solve a simultaneous system.

Now study this page until it seems obvious: en.wikipedia.org/wiki/Polynomial_remainder_theorem