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Designed to practice sign analysis across intervals and translate between factored form and inequality solution 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do you find the solution to each polynomial inequality?","Question",{"text":63,"@type":64},"Factor the polynomial to identify its zeros, then determine where the expression is positive or negative on intervals and write the solution set using interval notation.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What information is needed to create a polynomial inequality from a given solution?",{"text":68,"@type":64},"Identify which intervals and points are included or excluded in the given solution set, then construct an inequality whose sign behavior matches those intervals.",{"name":70,"@type":61,"acceptedAnswer":71},"Why is interval notation used in these problems?",{"text":72,"@type":64},"Interval notation concisely represents all x-values that satisfy the inequality, including brackets or parentheses to show whether endpoints are 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inequality.  \n1) (x 􀀐 􀀗)(x 􀀎 􀀖) 􀀟 􀀓 2) (x 􀀐 􀀗)(x 􀀎 􀀔) 􀁴 􀀓  \n3) (x 􀀐 􀀔)(􀀖x 􀀐 􀀗) 􀁴 􀀓 4) (x 􀀎 􀀛)(x 􀀎 􀀕)(x 􀀐 􀀖) 􀁴 􀀓  \n5) x 􀀕 􀀎 􀀘x 􀀎 􀀗 􀁤 􀀓 6) x 􀀕 􀀐 􀀔􀀗x 􀀎 􀀗􀀜 􀁴 􀀓  \n7) x 􀀕 􀀐 􀀗x 􀀐 􀀖􀀕 􀀡 􀀓 8) x 􀀕 􀀎 􀀔􀀙x 􀀎 􀀕􀀗 􀀡 􀀙x  \n9) (x 􀀎 􀀘 )(x 􀀐 􀀕)(x 􀀐 􀀔)(x 􀀎 􀀔) 􀀟 􀀓 10) (x 􀀎 􀀛)􀀕 (x 􀀎 􀀘 )(x 􀀎 􀀚 ) 􀀕 􀁴 􀀓  \nCritical thinking question:  \n11) Write a polynomial inequality with the solution: {􀀐􀀔}∪{􀀕}∪[􀀖 , 􀁦)  \nKuta Software-Infinite Precalculus Name   \nPolynomial Inequalities Date  Period   \nSolve each inequality.  \n1) (x 􀀐 􀀗)(x 􀀎 􀀖) 􀀟 􀀓 2) (x 􀀐 􀀗)(x 􀀎 􀀔) 􀁴 􀀓  \n(􀀐􀀖 , 􀀗) (􀀐􀁦 , 􀀐􀀔] ∪ [􀀗 , 􀁦)  \n3) (x 􀀐 􀀔)(􀀖x 􀀐 􀀗) 􀁴 􀀓 4) (x 􀀎 􀀛)(x 􀀎 􀀕)(x 􀀐 􀀖) 􀁴 􀀓  \n(􀀐􀁦 , 􀀔] ∪ [~~ ~~􀀗􀀖~~ ~~ , 􀁦) [􀀐􀀛 , 􀀐􀀕] ∪ [􀀖 , 􀁦)  \n5) x 􀀕 􀀎 􀀘x 􀀎 􀀗 􀁤 􀀓 6) x 􀀕 􀀐 􀀔􀀗x 􀀎 􀀗􀀜 􀁴 􀀓  \n[􀀐􀀗 , 􀀐􀀔] (􀀐􀁦 , 􀁦)  \n7) x 􀀕 􀀐 􀀗x 􀀐 􀀖􀀕 􀀡 􀀓 8) x 􀀕 􀀎 􀀔􀀙x 􀀎 􀀕􀀗 􀀡 􀀙x  \n(􀀐􀁦 , 􀀐􀀗) ∪(􀀛 , 􀁦) (􀀐􀁦 , 􀀐􀀙) ∪(􀀐􀀗 , 􀁦)  \n9) (x 􀀎 􀀘 )(x 􀀐 􀀕)(x 􀀐 􀀔)(x 􀀎 􀀔) 􀀟 􀀓 10) (x 􀀎 􀀛)􀀕 (x 􀀎 􀀘 )(x 􀀎 􀀚 ) 􀀕 􀁴 􀀓  \n(􀀐􀀘 , 􀀐􀀔) ∪(􀀔 , 􀀕) {􀀐􀀛} ∪ {􀀐􀀚 } ∪ [􀀐􀀘 , 􀁦)  \nCritical thinking question:  \n11) Write a polynomial inequality with the solution: {􀀐􀀔}∪{􀀕}∪[􀀖 , 􀁦)  \nExample: (x 􀀎 􀀔)􀀕 􀂘 (x 􀀐 􀀕)􀀕 (x 􀀐 􀀖) 􀁴 􀀓  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaij8zvgXZvIP6","https://ap.wps.com/l/cbCaij8zvgXZvIP6","pdf",43362,"English","# Solve each inequality\n## Problems 1-10\n## Critical thinking question 11","[{\"question\":\"How do you find the solution to each polynomial inequality?\",\"answer\":\"Factor the polynomial to identify its zeros, then determine where the expression is positive or negative on intervals and write the solution set using interval notation.\"},{\"question\":\"What information is needed to create a polynomial inequality from a given solution?\",\"answer\":\"Identify which intervals and points are included or excluded in the given solution set, then construct an inequality whose sign behavior matches those intervals.\"},{\"question\":\"Why is interval notation used in these problems?\",\"answer\":\"Interval notation concisely represents all x-values that satisfy the inequality, including brackets or parentheses to show whether endpoints are included.\"}]","Polynomial Inequalities - Polynomial Inequalities Worksheet - Kuta Software-Infinite Precalculus | PDF",1791426912]