Enthusiast
|
For #3, I'm going to use a technique called splitting the middle term. If it's unfamiliar to you, let me know and I'll show a different way of doing it.
3) 3m2 + 13mn - 10n2
Do this mentally-multiply 3*(-10) to get -30, and think of pairs of numbers that multiply to give -30 that also add to give +13. Factors of -30 are 1 and -30, 2 and -15, 3 and -10, 5 and -6, 6 and -5, 10 and -3, 15 and -2, and 30 and -1. Of those pairs, 15 and -2 is the only one that also adds to give 13. Knowing that, I'm going to rewrite the problem a little differently:
3m2 - 2mn + 15mn - 10n2
The value hasn't changed-I've simply just "split" 13mn into (-2mn + 15mn). From there, we can group those 4 terms into pairs, like this:
(3m2 - 2mn) + (15mn - 10n2)
Looking at the first set of parantheses, you want to ask yourself what factors are in both 3m2 and -2mn. In this case, there is an m in each, so we can factor out an m:
m(3m - 2n).....
In the second paratheses, we can factor out 5n, giving:
... 5n(3m - 2)
Putting both of these together, we get
m(3m - 2) + 5n(3m - 2)
Now we have 2 distinct terms, both with (3m - 2) as a factor, so we can factor out (3m - 2). Doing that gives us the final answer:
(3m - 2)(m + 5n)
#6a can be done using the same method.
5a) x + 3x/4
Since there is an x in both terms, try factoring that x out. When you factor x out of 1x, you're left with 1, and when you factor x from 3x/4, you're left with 3/4. So, it looks something like this:
x(1 + 3/4)
Since 1 + 3/4 is just 7/4, our final answer is:
7x/4
|
