Q. 55.0( 1 Vote )

If the polynomials x3 + 3x2 – m and 2x3 – mx + 9 leaves the same remainder when they are divided by (x – 2), find the value of m. Also find the remainder

Answer :

x3 + 3x2 – m and 2x3 – mx + 9 is divided by (x – 2) and the remainder is same.


Now let p(x) = x3 + 3x2 – m is divided by x – 2 then, p(2) is the remainder


p(2) = (2)3 + 3(2)2 – m


= 8 + 12 – m


= 20 – m


Now let q(x) = 2x3 – mx + 9 is divided by x – 2 then, q(2) is the remainder


q(2) = 2(2)3 – m(2) + 9


= 16 – 2m + 9


= 25 – 2m


Now, as the question says that the remainder for p(x) and q(x) is same


Therefore, p(2) = q(2)


20 – m = 25 – 2m


2m – m = 25 – 20


m = 5


Remainder = p(2) = 20 – m


= 15


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