There is this one trinomial that I can't seem to factor.
30x^2 -34x - 84
When I checked my final answer (added the inner numbers and outer numbers of the final binomial), I did not get -34.
Help is greatly appreciated.
The first set must multiply to make 15 (as in a and c in my example below).
The second set must multiply to make 42 (as in b and d below). This is what you're used to doing by the looks of things
Since a trinomial can be written as we expand this to give .
Factors of 42: 1, 2, 6, 7 , 21, 42
Factors of 15: 1, 3, 5, 15
It's very unlikely to be any of the extrema so pick the middle pairs first.
For your sum you need to find when it is known that and
as e^(i*pi) showed,
you are looking for 4 values a, b, c and d.
But there are only 3 terms in the equation, so we don't have enough clues to solve
using a few simultaneous equations.
Hence it's necessary to examine how they combine.
You need to factorise -42 and 15 and combine these two sets of factors
within parentheses as already shown to achieve -17x.
This is because -42 and 15 themselves do not combine to give -17x.
Usually these will be the most obvious ones, like 5 and 3, 6 and 7.
and in this case they are!
It doesn't always happen to be the most expected ones,
but that's normally the best place to start.