When $x^{3} + 3 x^{2} - m x + 4$ is divided by x- 2, the remainder is m + 3 find the value of m.

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Solution

Let f(x) = $x^{3} + 3 x^{2} - m x + 4$
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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When x3+3x2−mx+4 is divided by x- 2, the remainder is m + 3 find the value of m.

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

When $x^{3} + 3 x^{2} - m x + 4$ is divided by x- 2, the remainder is m + 3 find the value of m.

Let f(x) = $x^{3} + 3 x^{2} - m x + 4$
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