my teacher taught our class how to factorize using the criss cross method, and I did not understand what she tried to communicate to the class. The equation I am trying to solve as an example is $7x^2 - 9x + 2$. What exactly is the method for this?
Regards,
1 Answer
Given your quadratic $7x^2-9x+2$, you need to think of two numbers $a$ and $b$ such that $a\times b=7$, and two numbers $c$ and $d$ such that $c\times d=2$, and $ad+bc=-9$.
It takes some time and practice to start seeing what numbers work. For example, letting $a=1, b=7, c=-1, d=-2$ works because $ab=1\times 7=7$, $cd=-1\times -2=2$, and $ad+bc=1\times-2+7\times-1=-2-7=-9$.
In general for a quadratic of the form $\alpha x^2+\beta x+\gamma$, you want $ab=\alpha$, $cd=\gamma$ and $ad+bc=\beta$, where $\alpha,\beta, \gamma\in\mathbb{R}.$
