Question

It is given that (x − 2) is a factor of polynomial 2x3 − 7x2+ kx − 2.

Find:

1. the value of ‘k’. 
2. Hence, factorise the resulting polynomial completely.

Answer 1

Given:

first term a = 5 last term l = 50 and sum Sn = 440

Using the sum formula of an A.P.,

`S_n = n/2(a + l)`

= 440 = `n/2 (5 + 50)`

`440 = (55n)/2`

`n = 880/55 = 16`

Thus, the number of terms is 16.

(b) Using the nth term formula,

l = a + (n − 1)d

50 = 5 + (16 − 1)d

45 = 15d

d = 3

Hence, the common difference is 3.