How do you find all values of k so that the polynomial $x^2-8x+k$ can be factored with integers?

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Answer 1 · 2017-08-16T14:16:26

$k = {16,15,12,7,0}$

Solving for $x$ we have

$x = 4pm sqrt(16-k)$

If $x$ is integer then $16-k = n^2 ge 0$ or

$k le 16-n^2$ then

$n = {0,1,2,3,4}$ we have

$k = {16,15,12,7,0}$

How do you find all values of k so that the polynomial x^2-8x+kx^2-8x+k can be factored with integers?