Consider the quadratic expression

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

x^{2}+kx+24

, where

k

is an integer. (i) List all possible ordered pairs of integers

(r,s)

whose product is

24

. (ii) For each pair

(r,s)

obtained in part (i), write the corresponding value of

k

and the factorised form of

x^{2}+kx+24

. (iii) Hence, determine all integer values of

k

for which

x^{2}+kx+24

can be expressed as a product of two linear factors with integer coefficients.