1)Let and . What is the coefficient of in the sum ?
2)Let and . Let be a constant. What is the largest possible degree of ?
3)Let and . Let be a constant. What is the smallest possible degree of the polynomial ?
4)Let and . What is the degree of ?
5)Find if the expansion of the product of and has no term.
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All we have to do is add the coefficients of the x^3 terms, or 1 + 5 = 6.
Because a is a constant, the largest possible must be 4, as a cannot change the degree.
We want to have the smallest possible degree, so we should cancel terms. So, we set b = -1/2 and the degree of the sum is 1.
To find the degree of the porduct, we just add the degrees of the functions. So, our answer is 4 + 4 = 8.
We can find which terms multiply to get something with x^2 in it. We get 28 + 2t - 5 = 0, or 23 + 2t = 0 => t = -11.5.
Hoping this helped,