Question

What number should be subtracted from x³ + 3x² – 8x + 14 so that on dividing it by x – 2, the remainder is 10? 

Answer 1

Let the number to be subtracted be k and the resulting polynomial be f(x). 

So, f(x) = x³ + 3x² – 8x + 14 – k 

It is given that when f(x) is divided by (x – 2), the remainder is 10. 

∴ f(2) = 10   

(2)³ + 3(2)² – 8(2) + 14 – k = 10 

8 + 12 – 16 + 14 – k = 10 

18 – k = 10

– k = 10 – 18 = – 8

k = 8 

Thus, the required number is 8.