Find t if the expansion of the product of x^3 - 4x^2 + 5x - 5 and x^2 + tx - 7 has no x^2 term.
The $x^2$ term is $(-4x^2)(-7) + (5x)(tx) + (-5)(x^2)$ which is equal to $(28+5t-5)x^2$. Since the product has no $x^2$, we have $28+5t-5=0$. Solving for $t$ gives $t=-23/5$.
