1) Let $f(x) = x^4-3x^2 + 2$ and $g(x) = 2x^4 - 6x^2 + 2x -1$. Let $b$ be a constant. What is the smallest possible degree of the polynomial $f(x) + b\cdot g(x)$?
2)Suppose is a polynomial such that , , , and . What is the sum of the coefficients of ?
3)Let and . Let be a constant. What is the largest possible degree of ?
4)Let be a quadratic polynomial such that , and Let Find the sum of the coefficients of the terms in with even exponents. (For example, the sum of the coefficients of the terms in with even exponents is )
Thank you!
+36916 1) if b = -1/2 when yo add the two polynomials together the 4 and the 2 dgrees 'cancel out' and you are left with degree of one ; x1
