When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m. - Mathematics

When x³ + 3x² – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.

Sum

Let f(x) = x³ + 3x² – mx + 4

According to the given information,

f(2) = m + 3

(2)³ + 3(2)² – m(2) + 4 = m + 3

8 + 12 – 2m + 4 = m + 3

24 – 3 = m + 2m

3m = 21

m = 7

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