Can you find the value of k?

Question

When $2 x^{4} - k x^{3} + 3 x^{2} - x$ $2x^4-kx^3+3x^2-x$ is divisible by $x - 3$ $x-3$

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Answer 1 · 2018-03-26T08:10:40

$color(magenta)(k=186/27 or k=6.8888...$

Since $x-3$ is a factor of $2x^4−kx^3+3x^2−x$ when you plug in $x=3$

$2(3)^4−k(3)^3+3(3)^2−(3)=0$

$2(81)-k(27)+3(9)-3=0$

$162+27-3=27k$

$27k=186$

$k=186/27$

$color(magenta)(k=186/27 or k=6.8888...$

~Hope this helps! :)