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Students solve a set of quadratic equations labeled 1–20, including cases with linear factors, products set to zero, and equations requiring factoring after rearrangement. The sheet also includes critical thinking true/false prompts about when factored quadratics with real-number factors cannot have imaginary solutions versus when unfactorable quadratics must have imaginary solutions. 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True/False.  \n19) If a quadratic equation can be factored and 20) If a quadratic equation cannot be factored then  \neach factor contains only real numbers then it will have at least one imaginary solution.  \nthere cannot be an imaginary solution.  \nKuta Software-Infinite Algebra 2 Name___________________________________  \nSolving Quadratic Equations By Factoring Date________________ Period____  \nSolve each equation by factoring.  \n1) (3n − 2)(4n + 1) = 0 2) m(m − 3) = 0  \n{~~ ~~23~~ ~~ , − ~~ ~~14~~ ~~ } {3, 0}  \n3) (5n − 1)(n + 1) = 0 4) (n + 2)(2n + 5) = 0  \n{~~ ~~ ~~ ~~   \n15 , −1 } {−2, − 52 }  \n5) 3k2 + 72 = 33k 6) n 2 = −18 − 9n  \n{3, 8} {−6, −3}  \n7) 7v2 − 42 = −35v 8) k2 = −4k − 4  \n{−6, 1} {−2}  \n9) −2v2 − v + 12 = −3v2 + 6v 10) −4n2 + 6n − 16 = −5n2  \n{3, 4} {2, −8}  \n11) 8r2 + 3r + 2 = 7r2  \n{−2, −1}  \n13) 10n2 − 35 = 65n  \n{− ~~ ~~12~~ ~~ , 7 }  \n15) 16n2 − 114n = −14  \n18~~ ~~ , 7 }  \n{  \n17) 7a2 + 32 = 7 − 40a  \n{− ~~ ~~57~~ ~~ , −5 }  \nCritical thinking questions. True/False.  \n19) If a quadratic equation can be factored and each factor contains only real numbers then there cannot be an imaginary solution.  \n12) b 2 + b = 2  \n{−2, 1}  \n14) 3x2 − 8x = 16  \n{− ~~ ~~43~~ ~~ , 4 }  \n16) 28n2 = −96 − 184n  \n{− ~~ ~~47~~ ~~ , −6 }  \n18) 42x2 − 69x + 20 = 7x2 − 8  \n{~~ ~~75~~ ~~ , 47~~ ~~ }  \n20) If a quadratic equation cannot be factored then it will have at least one imaginary solution.  \nFalse (Example, x2 = 10)  \nTrue  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiplTU4040XOJ","https://ap.wps.com/l/cbCaiplTU4040XOJ","pdf",33981,"English","# Solve Each Equation by Factoring\n## Critical Thinking Questions: True/False","[{\"question\":\"What does the worksheet ask students to do with each quadratic equation?\",\"answer\":\"Students solve each quadratic equation by factoring, using algebraic manipulation to rewrite expressions into factorable forms.\"},{\"question\":\"How are the equations organized on the worksheet?\",\"answer\":\"The worksheet lists multiple quadratic equations numbered 1 through 20, followed by critical thinking true/false statements.\"},{\"question\":\"What do the critical thinking true/false questions test?\",\"answer\":\"They test understanding of the relationship between factorability over real numbers and the presence or absence of imaginary solutions.\"}]","Quadratic Equations By Factoring - Solving Quadratic Equations By Factoring Worksheet | PDF",1791426114]