Using remainder theorem, find the value of m if the polynomial
$f(x) = x^{3} + {5x}^{2} - mx + 6$ leaves a remainder $2 m$ when divided by ( $x-1$ ).

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Solution

Given: $f(x) = x^{3} + {5x}^{2} - mx + 6$ , divisor = $(x-1)$ , and
remainder = $2m$

From remainder theorem, we know that
when a polynomial $f(x)$ is divided by $(x-a)$ , the
remainder is $f(a)$ .

$∴ f(1) = 2 m$
$(1) ³ + 5 (1) ² - m (1) + 6 = 2 m$
$1 + 5 - m + 6 = 2 m$
$3 m = 12$
$m = 4$

Hence, the value of m is $4$ .

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Remainder Theorem

Standard IX Mathematics

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Using remainder theorem, find the value of m if the polynomial ​ f(x)=x3+5x2−mx+6 leaves a remainder 2m when divided by (x-1).

Given: f(x)=x3+5x2−mx+6, divisor = (x-1), and remainder = 2m From remainder theorem, we know that when a polynomial f(x) is divided by (x-a), the remainder is f(a). ∴f(1)=2m (1)³+5(1)²−m(1)+6=2m 1+5−m+6=2m 3m=12 m=4 Hence, the value of m is 4.

Using remainder theorem, find the value of m if the polynomial
$f(x) = x^{3} + {5x}^{2} - mx + 6$ leaves a remainder $2 m$ when divided by ( $x-1$ ).