Let f (x) %3D 1 + 2x The coefficient of x* in the 8th Taylor polynomial pg is (No Response). (Write your answer as an integer.)

Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 X 0.4 0.8 1.2 1.6 2 Ly 0 0.25 1 2.25 4 6.25

1. Consider the polynomial f(x) = (x – 1)(x+2)(x- 3)(x+5). A. What are the roots of f? B. Suppose you were to multiply the polynomial out; what would the leading coefficient of f be? C. Suppose you were to multiply the polynomial out; what would the constant term of f be?

(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.

6. Which polynomials have 4 roots? Select all that apply. 3x* – 81 = 0 4x + 4x + 4 = 0 2x4 + 3x? + 4x = 0 x* + 5x – 10 = 0

The polynomial x2 - 2x - 3 is irreducible (over R). Select one: O True O False

Let f(x) = , find L, (x) of the second Lagrange interpolating polynomial, if x, =2, x, =2.5, X2 =4 Select one: a. (x - 6.5)x + 10, b. (0.05x - 0.425)x + 1.15 (-4x + 24)x – 32 3 (x – 4.5)x + 5 O d. 3

Consider the polynomial defined by p(x) = (x − a)(x − b) ... (x − z). a. How many additions and multiplications are involved in this calculation? Explain. b. Calculate p(7).

B4. Use a Taylor polynomial to get a rational number that approximates √e with accu- racy 10-4.

Show that the given values for a and b are lower and upper bounds for the real zeros of the polynomial. P(x) = 2x3 + 9x2 + 3x – 4; a = -5, b = 1 for a = -5: -5[ 2 9. 3 -4 Since the row containing the quotient and remainder has ---Select-- a = -5 is | ---Select--- for b = 1: 1 2 Since the row containing the quotient and remainder has --Select--- b = 1 is -Select---