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

Question

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

Answers

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

Explanation:

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}#


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