What is the negation of this statement? Fþr all polynomials p: R-R there exists ɛ> 0 and & > 0 and R >0 such that for all x> R the following is true: Ifxsysxtô, then we have p(x)-p(y)

A boy has a collection of 20 pennies, 8 nickels, 10 dimes and 15 quarters. How many coinsmust the boy take from his collection to be certain that he has(a) 12 coins of the same kind?(b) 10 pennies, 5 nickels, 6 dimes or 8 quarters?(c) 15 pennies, 10 nickels, 12 dimes or 8 quarters?

(1) For each member of your group record their response to: “ Give an example of a polynomial and an expression involving x that is not a polynomial." (2) A box with no top is to be fashioned from an 18 inch x 24 inch piece of cardboard by cutting out congruent squares from each corner of the cardboard and then folding the resulting tabs. Let x denote the length of the side of the square which is removed from each corner. Determine a polynomial which gives the vol- ume of the box as a function of x. Use a plot of this polynomial to determine the optimal value of x.

Which of the following polynomials is reducible over Q: x3 +2 x4 + 3 x5 + 1 x2 + 3 I thought it was x4 + 3 but that was wrong.  Is it x5 + 1?