$It is given that (x-1) is a factor of the$
$polynomial f (x) = x^{3} + 13 x^{2} + 31 x - k .$
$The value of k is:$

[1 Mark ]

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Solution

The correct option is A 45
Given,

$(x - 1)$ is a factor of the polynomial
$f (x) = x^{3} + 13 x^{2} + 31 x - k$

$∴ x = 1$ satisfies the equation
$x^{3} + 13 x^{2} + 31 x - k = 0$

$\Rightarrow (1)^{3} + 13 (1)^{2} + 31 (1) - k = 0$

$\Rightarrow 1 + 13 + 31 - k = 0$

$\Rightarrow k = 45$

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Similar questions

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It is given that (x-1) is a factor of the polynomial f(x)=x3+13x2+31x−k. The value of k is: [1 Mark ]

The correct option is A 45Given, (x−1) is a factor of the polynomial f(x)=x3+13x2+31x−k ∴x=1 satisfies the equation x3+13x2+31x−k=0 ⇒(1)3+13(1)2+31(1)−k=0 ⇒1+13+31−k=0 ⇒k=45

$It is given that (x-1) is a factor of the$
$polynomial f (x) = x^{3} + 13 x^{2} + 31 x - k .$
$The value of k is:$

[1 Mark ]

The correct option is A 45
Given,

$(x - 1)$ is a factor of the polynomial
$f (x) = x^{3} + 13 x^{2} + 31 x - k$

$∴ x = 1$ satisfies the equation
$x^{3} + 13 x^{2} + 31 x - k = 0$

$\Rightarrow (1)^{3} + 13 (1)^{2} + 31 (1) - k = 0$

$\Rightarrow 1 + 13 + 31 - k = 0$

$\Rightarrow k = 45$