Q. 55.0( 1 Vote )

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

Answer :

x^{3} + 3x^{2} – m and 2x^{3} – mx + 9 is divided by (x – 2) and the remainder is same.

Now let p(x) = x^{3} + 3x^{2} – 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) = 2x^{3} – 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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