Problem 2: (a) Use properties of quadratic functions to prove that 5x² > (x+1)² for all real x > 1. (b) Use mathematical induction and the inequality from part (a) to prove that 3 - 5" > 4n+1 + n² for all integers n > 2.

Let q(n) be the sum of the squares of the first n odd numbers. For example: q(0)  =  0 q(1)  =  12 q(2)  =  12 + 32 q(3)  =  12 + 32 + 52 q(4)  =  12 + 32 + 52 + 72   ⋮   What would be the closed-form expression for q(n), where n is any integer greater than or equal to 0? Your expression must work for any such n, not just those shown in the examples.

QUESTION 14 /hich of the following is a factor of 2x-18x'+40x? O(x+4) Ox-8) O(x-20) O (x-5) O(2x+5)

Need only a handwritten solution only (not a typed one).