Factoring

[Jesse598]

Factor the following trinomial. 3x² − xy − 114y²

I don't understand how to do this!!!!:evil: I multiplied 114 with 3 which equals -352, and then I was wondering what multiplies into 352, but adds to be -1? I'm confused.

 

[soroban]

Hello, Jesse598!

Factor: \(\displaystyle 3x^2 -xy - 114y^2\)
I don't understand how to do this!
I multiplied -114 with 3 which equals -342,
and then I was wondering what multiplies to 342, but adds to be -1?

We want to factor 342 into two parts whose difference is 1.


Divide 342 by 1, 2, 3, ...
. . and keep the ones that "come out even".


. . \(\displaystyle \begin{array}{cc} \text{Division} & \text{Factors} \\ \hline 342 \div 1 \:=\:342 & (1,342) \\ 342 \div 2 \:=\:171 & (2,171) \\ 342 \div 3 \:=\:114 & (3,114) \\ 342 \div 4 \:=\;\;\;?\;\; & \cdots \\ 342 \div 5 \:=\;\;\;?\;\; & \cdots \\ 342 \div 6 \:=\:57\;\; & (6,57) \\ \vdots & \vdots \\ 342 \div 9 \:=\:38 & (9,38) \\ \vdots & \vdots \\ 342 \div 18 \:=\:19 & {\bf(18,19)} \end{array}\)
. . . . . . . . . . . . . . . . . . \(\displaystyle \uparrow\)
. . . . . . . . . . . . . . . . \(\displaystyle \text{There!}\)

 

[mmm4444bot]

keep the ones that "come out even"

Ahem. Ones are always odd.