Use synthetic division to perform each division. Consider the polynomial function (x) = x 3 - 5x 2 + 2x + 7. (a) Use the

Use synthetic division to perform each division.

Consider the polynomial function ƒ(x) = x³ - 5x² + 2x + 7.

(a) Use the intermediate value theorem to show that ƒ has a zero between 1 and 2.

(b) Use Descartes’ rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros.

(c) Use a graphing calculator to find all real zeros to as many decimal places as the calculator will give.