How do you find all values of k so that the polynomial #x^2-8x+k# can be factored with integers? Algebra Polynomials and Factoring Factorization of Quadratic Expressions 1 Answer Cesareo R. Aug 16, 2017 #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}# Answer link Related questions How do you factor trinomials? What is factorization of quadratic expressions? How do you factor quadratic equations with a coefficient? What are some examples of factoring quadratic expressions? How do you check that you factored a quadratic correctly? How do you factor #x^2+16x+48#? How do you factor #x^2-9x+20#? Question #3fdac How do you factor #8+z^6#? There is no GCF to be factor out, so is there another method to complete this? How do you factor #2t^2+7t+3#? See all questions in Factorization of Quadratic Expressions Impact of this question 4185 views around the world You can reuse this answer Creative Commons License