Question

If the polynomials $x^3 + 3 x^2 - m$ and $2x^3 - mx + 9$ leave the same remainder when they are divided by $(x - 2)$, find the value of $m$. Also find the remainder.

Answer 1

When $x^3 + 3 x^2 - m$ is divided by (x – 2) then the remainder is 

$(2)^3 + 3(2)^2 - m$
 
8 + 12 – m

20 – m

When $2x^3 - mx + 9$ is divided by (x – 2) then the remainder is 

$2(2)^3 - m(2) + 9$
 
16 + 9 – 2m

21 – 2m

As per the question, the two remainders are equal.

20 – m = 21 – 2m

m = 1

Remainder = 21 – 2(1) = 19