What is the value of $k$ $k$ for which $(x - 1)$ $(x-1)$ is a factor of $(2 x^{3} + 9 x^{2} + x + k)$ $(2x^3+9x^2+x+k)$ ?

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What is the value of $k$ $k$ for which $(x - 1)$ $(x-1)$ is a factor of $(2 x^{3} + 9 x^{2} + x + k)$ $(2x^3+9x^2+x+k)$ ?

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Answer 1 · 2017-10-11T21:40:04

$k = - 12$ $k = -12$

Explanation:

$f (x) = 2 x^{3} + 9 x^{2} + x + k$ $f(x) = 2x^3 + 9x^2 + x + k$

If $(x - 1)$ $(x-1)$ is a factor, then making $x = 1$ $x = 1$ would make $(x - 1)$ $(x-1)$ equal to 0, and everything else in the equation multiply by that 0, resulting to $f (1) = 0$ $f(1) = 0$ .

$f (1) = 2 \cdot 1^{3} + 9 \cdot 1^{2} + 1 + k = 0$ $f(1) = 2*1^3 + 9*1^2 + 1 + k = 0$

$f (1) = 2 + 9 + 1 + k = 0$ $f(1) = 2+9+1+k = 0$

$k = - (2 + 9 + 1) = - 12$ $k = -(2+9+1) = - 12$

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What is the value of $k$ $k$ for which $(x - 1)$ $(x-1)$ is a factor of $(2 x^{3} + 9 x^{2} + x + k)$ $(2x^3+9x^2+x+k)$ ?

1 Answer

Explanation:

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