Math Insπres - Math Inspires
Explain how to solve for all the roots of the following polynomial function. Write your explanation as if you were teaching this problem to a classmate of yours who had been absent. This assignment will be assessed on how well you are able to convey your ideas in complete sentences with your work shown along the way.fx=x3+6x-20 Vocabulary Words: Factor, Root, Zero, Cubic, Function, Degree, Complex Roots, Real Roots, Rational RootsExplain how to solve for all the roots of the following polynomial function. Write your explanation as if you were teaching this problem to a classmate of yours who had been absent. This assignment will be assessed on how well you are able to convey your ideas in complete sentences with your work shown along the way.fx=x3+6x-20 Vocabulary Words: Factor, Root, Zero, Cubic, Function, Degree, Complex Roots, Real Roots, Rational RootsPut the steps in order:We need to use synthetic division to factor the polynomial. 320040022860Note, while dividing synthetically we plug in a zero since there is no quadratic term.00Note, while dividing synthetically we plug in a zero since there is no quadratic term.(x3+6x-20)÷(x-2) Since we are unable to factor the polynomial, we will enter it into the graphing calculator and check the graph to find the real roots. The roots of the polynomial function: fx=x3+6x-20 are: The graph crosses the x-axis once at x = 2. The only real root in this graph on the right is x = 2.Since the polynomial is a degree three polynomial (cubic polynomial), this means that there may be up to three complex roots. Further, x = 2 is a zero with multiplicity 1 since the graph has no bends and passes thorough the x-axis (no even multiplicity since the graph does not bounce off the x-axis). Since one root is real, we could have 2 non-real roots.Check to see if you can factor the polynomial. It is a cubic trinomial with no GCF so we cannot factor it.We need to use the quadratic formula to solve for the non-real roots of x2+2x+10.571500673100x =5143500-37465000Find all of the roots of the polynomial: fx=x3-5x2+10x -6Sam thinks there is a triple root at 1.? Identify whether Sam is correct or incorrect and use mathematical reasoning, evidence and vocabulary to explain why. ? If Sam is incorrect, find the correct solution by showing work and providing reasoning.Student Rubric: Each box will be graded individually and then divided by 4.Make a ConjectureCorrect or Incorrect solution identified accurately1 pointMath VocabularyCommunicate precisely using Math Vocabulary appropriately1 pointProvide Evidence to support your ConjectureProvide evidence from graph, formulas or properties2 pointsClear and Complete Mathematical ReasoningExplanation provides sufficient justification for whether or not the answer is accurate2 pointsTeacher Rubric: Score each box individually and then divide total by 4.HSA-AP.B. Understand the relationship between zeros and factors of polynomials.HSA-APR.B.2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).HSA-APR.B.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.Reasoning with Equations & InequalitiesHSA-REI.D. Represent and solve equations and inequalities graphically.HSA-REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.HSF-IF.C. Analyze functions using different representations.HSF-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.HSF-IF.C.7c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.Make a ConjectureCorrect or Incorrect ConjectureCorrect or Incorrect solution identified accurately 1 pointMath Vocabulary Communicate precisely using Math Vocabulary appropriatelyCommunicate precisely using Math Vocabulary appropriately: factoring, synthetic division, substitution, zeros, roots, real, imaginary1 pointProvide Evidence to support your ConjectureFormulas, Pictures, PropertiesProvide evidence from graph, formulas or propertiesFull Points for providing sufficient evidence, one point for referencing a property or graph accurately.2 pointsClear and Complete Mathematical Reasoning Connect the evidence to the problemExplanation provides sufficient justification for whether or not the answer is accurateOne point for incomplete but correct reasoning even if solution is not identified accurately.2 pointsGrowth: A 2 Point increase is considered growth. ................
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