If you were an Algebra 1 instructor and were creating a test on factoring trinomials of the form ax2 + bx + c, what do you think would be the easiest way to create a trinomial that can be factored? Provide one unique example.
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If you meant equations only dealing with x on the left-hand side, then these are other, simple possibilities:
\[(x+1)^2 = x^2 + 2x + 1\]
\[(x+1)(x-1) = x^2 -1\]
\[(x-1)^2 = x^2 -2x + 1\]
He'll likely use one that's of this form, but with additional numbers in front of the first x term, for instance.
I would choose any equation that looked like it was already factored, and then expand it out. Basically something of them form \[(x+a)(x+b)\]where \(a\) and \(b\) are constant (integers).
An example would be to take \(a=-3,\; b=2\). So\[(x-3)(x+2)\]\[x^2-3x+2x-6\]\[x^2-x-6\] So my question would ask to factor \(x^2-x-6\)