Find the greatest common factor in each equation and factor them out to determine
all possible solutions for each given variable. Do a check and plug in each of your
possible solutions for the given variable in the equation to see if it makes the
equation a true statement.
12c^2 + 36c = 0
8p^2– 72p = 0
Help me. You can do one or both?
Details:
Answers (1)
12c^2 + 36c = 0 You look and see that all the numbers are multiples of 12.
12(c^2 + 3c) = 0 The rule is you can do any valid operation on both sides of an equation and it will still be equal. Divide by 12.
c^2 + 3c = 0 Now you notice that you can divide by c, but this is called "snake in the deal". That means you are going to get bit if you don't watch out.
c + 3 = 0
c = -3
BUT:
c(c + 3) = 0 is also true when c=0 and the first answer did not reveal that. You have to remember that an equation with x^n has n factors, and you have to account for all of them.
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
Thanks