13. Writ a polynomial f(x) in general form that has the following characteristics

Degree 3 Leading coefficient of 8 One double root at x = 4 One root at x = 3/2

14. Degree 5. Roots of multiplicity 2 at x = 3 and x = 2 and a root of multiplicity 1 at x = 2. y-intercept at (x, y) = (0, 64).

15. f(x) = 2x³ 7x 1 Find the Approximate the local minimum And local maximum (Round your answers to two decimal places.

16. A rectangle has a length of 12 units and a width of 9 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to creat an open box. Express the volume V of the box as a polynomial function in terms of x.

17. A square has sides of 22 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to creat an open box. Express the volume V of the box as a function in terms of x.

18. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.

section 3.5

8. Use the given length and area of a rectangle to express the width algebraically. (Simplify your answer completely.)Length is 3x 4, area is 6x⁴ 8x³ + 9x² 3x 12