Question

The remainder of polynomial q(x)=x^3+mx^2-3x+7 is -2 when divided by (x+3)
Remainder obtained when q(x) is divided by (x-4) is

Answer 1

Answer:

75

Step-by-step explanation:

Answer 2

$Given \: polynomial \: q(x) = x^{3}+mx^{2}-3x+7$

$If \: q(x) \: is \: divided \: by \: (x+3) \: the \\ Remainder \: is \: q(-3)$

$But\: q(-3) = -2 \: (given)$

$\implies (-3)^{3}+m(-3)^{2}-3(-3)+7 = -2$

$\implies -27 + 9m + 9 + 7 = -2$

$\implies 9m - 27 + 16 = -2$

$\implies 9m - 11= -2$

$\implies 9m = -2 + 11$

$\implies 9m = 9$

$\implies m = \frac{9}{9}$

$\implies \green {m = 1}$

/* Put m = 1 in q(x) , we get */

$\blue { q(x) = x^{3}+x^{2}-3x+7 }$

$Now, If \: q(x) \:divided \:by \: (x-4) \: then \:the \\remainder \: is \: q(4)$

$\red{ Remainder q(4) } \\= 4^{3} + 4^{2} - 3\times 4 + 7 \\= 64 + 16 - 12 + 7 \\= 80 - 5 \\= 75$

Therefore.,

$\red { Value \: of \:m } \green { = 1 }$

$\red { And \: Required \: Remainder } \green { = 75 }$

•••♪