The product of 3t^2 + 5t + a and 4t^2 + bt - 2 is 12t^4 + 38t^3 + 8t^2 - 34t + 8. What is a + b?
+128408 (3t^2 + 5t + a) ( 4t^2 + bt - 2)
3t^2 ( 4t^2 + bt - 2) = 12t^4 + 3bt^3 - 6t^2
5t ( 4t^2 + bt - 2) = 20t^3 + 5bt^2 - 10t
a ( 4t^2 + bt - 2) = 4at^2 + abt - 2a
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12t^4 + (3b + 20)t^3 + ( 4a + 5b - 6)t^2 + (ab - 10) t - 2a
Equate terms
-2a = 8 ab - 10 = -34
a = -4 -4b - 10 = -34
-4b = -24
b = 6
a + b = -4 + 6 = 2
