Find $t$ if the expansion of the product of $x^3 - 4x^2 + 2x - 5$ and $x^2 + tx - 7$ has no $x^2$ term.
This is a very simple way to solve it:
We know that the x^2 terms come from: (-4)*(-7)+2t+(-5)*1
28 + 2t -5
23 + 2t
If we want this equal to zero, we must have 23+2t = 0
t = -11.5
Hope this helped!