When \[{{\mathbf{x}}^{\mathbf{3}}}~+\text{ }\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{4}\]is divided by \[\mathbf{x}\text{ }\text{ }\mathbf{2}\], the remainder is \[\mathbf{m}\text{ }+\text{ }\mathbf{3}\]. Find the value of m. - Noon Academy

When

${{\mathbf{x}}^{\mathbf{3}}}~+\text{ }\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{4}$

is divided by

$\mathbf{x}\text{ }\text{ }\mathbf{2}$

, the remainder is

$\mathbf{m}\text{ }+\text{ }\mathbf{3}$

. Find the value of m.

Class 10 | Exercise 8C | ICSE | Maths | Remainder and Factor Theorems | Selina

When

${{\mathbf{x}}^{\mathbf{3}}}~+\text{ }\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{4}$

is divided by

$\mathbf{x}\text{ }\text{ }\mathbf{2}$

, the remainder is

$\mathbf{m}\text{ }+\text{ }\mathbf{3}$

. Find the value of m.

Let us consider f(x) =

${{\mathbf{x}}^{\mathbf{3}}}~+\text{ }\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{4}$

From the question, we have

$f\left( 2 \right)\text{ }=\text{ }m\text{ }+\text{ }3$

${{\left( 2 \right)}^{3}}~+\text{ }3{{\left( 2 \right)}^{2}}~\text{ }m\left( 2 \right)\text{ }+\text{ }4\text{ }=\text{ }m\text{ }+\text{ }3$

$8\text{ }+\text{ }12\text{ }\text{ }2m\text{ }+\text{ }4\text{ }=\text{ }m\text{ }+\text{ }3$

$24\text{ }\text{ }3\text{ }=\text{ }m\text{ }+\text{ }2m$

$3m\text{ }=\text{ }21$

Thus,

$m\text{ }=\text{ }7$

i

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