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.

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- Mar 8th 2010, 12:36 PMJayRich88Factoring a Trinomial
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. - Mar 8th 2010, 12:42 PMpickslides
- Mar 8th 2010, 12:45 PMe^(i*pi)
First of all I will factor out a 2 to make it easier

$\displaystyle 2(15x^2-17x-42)$

Check which numbers are factors of 42 and which make 15

$\displaystyle 15 = 3 \times 5$

$\displaystyle 42 = 7 \times 6 $

We know the signs in the brackets are opposite because we get -42 not 42.

Afterwards it's trial and error, keep going until you get the answer like mine below.

$\displaystyle 2(5x+6)(3x-7) = 2(15x^2-35x+18x-42) = 2(15x^2-17x-42) = 30x^2-34x-84$ - Mar 8th 2010, 12:57 PMJayRich88
- Mar 8th 2010, 01:16 PMe^(i*pi)
Factors of 42 won't add up to 15. What you're looking for is two sets of numbers

*independent of each other*.

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 $\displaystyle (ax+b)(cx+d)$ we expand this to give $\displaystyle (ac)x^2 + (ad+bc)x + (bd)$.

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 $\displaystyle ad+bc = -17$ when it is known that $\displaystyle ac = 15$ and $\displaystyle bd =-42$ - Mar 8th 2010, 01:44 PMArchie Meade
Hi JayRich88,

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.