Consider the cubic polynomial

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

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.