Mathematics

Problem

Consider the cubic polynomial

3x^{3}+p\,x^{2}+q\,x-40

. It is known that two of its zeroes are

2

and

-5

. a. Verify that

(x-2)(x+5)

is a factor of the polynomial. b. Determine the values of

p

and

q

. c. Find the third zero of the polynomial. d. Express the polynomial as a product of its linear factors.