If $(x - 1)$ divides $m x^{3} - 2 x^{2} + 25 x - 26$ with remainder $0$ , find the value of $m$ .

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Solution

According to remainder theorem, when $f (x)$ is divided by $(x - 1)$
Remainder $= f (1) = 0$ (given).

$f (x) = m x^{3} - 2 x^{2} + 25 x - 26$
$f (1) = m (1)^{3} - 2 (1)^{2} + 25 (1) - 26$
$⟹ 0 = m - 2 + 25 - 26$
$⟹ m - 3 = 0$
$⟹ m = 3$

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If (x−1) divides mx3−2x2+25x−26 with remainder 0, find the value of m.

According to remainder theorem, when f(x) is divided by (x−1)Remainder =f(1)=0(given).f(x)=mx3−2x2+25x−26f(1)=m(1)3−2(1)2+25(1)−26⟹0=m−2+25−26⟹m−3=0⟹m=3

If $(x - 1)$ divides $m x^{3} - 2 x^{2} + 25 x - 26$ with remainder $0$ , find the value of $m$ .

According to remainder theorem, when $f (x)$ is divided by $(x - 1)$
Remainder $= f (1) = 0$ (given).

$f (x) = m x^{3} - 2 x^{2} + 25 x - 26$
$f (1) = m (1)^{3} - 2 (1)^{2} + 25 (1) - 26$
$⟹ 0 = m - 2 + 25 - 26$
$⟹ m - 3 = 0$
$⟹ m = 3$