Other-Equations

Other-Equations - Other Algebraic Equations Including...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Other Algebraic Equations Including Factorable Higher Degree Polynomials, Rational Equations, Radical Equations, Equations With Rational Exponents, and Quadratic Form Equations Factorable Higher Degree Polynomials A factorable higher degree polynomial is defined here as one that has a greatest common monomial factor that factors out in such a way that the resulting factors consist of the monomial and a polynomial of degree 2 or less, allowing easy solution. Here is an example: 3x 4 - 2x 3 + x 2 = 0 may be factored as x 2 (3x 2 – 2x + 1) = 0 by applying the Distributive Property. Method For Solving These Factorable Higher Degree Polynomials 1. Move all terms to one side of = leaving 0 on one side using the Addition Property of Equality. 2. Factor out the greatest common factor using the Distributive Property. 3. Let each factor = 0 and solve each equation using an appropriate method. Example: Solve 2x 4 – 3x 3 = –x 2 2x 4 – 3x 3 = –x 2 Given 2x 4 – 3x 3 + x 2 = 0 Add x 2 to both sides using Addition Property of Equality x 2 (2x 2 – 3x + 1) = 0 Factor out x 2 using the Distributive Property x 2 = 0 and Apply the Zero Product Law 2x 2 – 3x + 1 = 0 Solve x 2 = 0 x = ±√ 0 x= 0 Extract Square Roots Solve 2x 2 – 3x + 1 = 0 (2x - 1)(x - 1) = 0 Factor using the Distributive Property x –1 = 0 Apply the Zero Product Law 2x – 1 = 0 x = 1 and x = ½ Solve using Addition and Division Properties of Equality The three solutions are x = 0, x = 1, and x = ½ Remember to find all three solutions – many students forget the zero solution!
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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Equations Containing Rational Expressions Equations containing rational expressions are here defined as those containing fractions with variables. For example, 1/x + 1/3 = 1/(x+1) would be such an equation. Method For Solving Equations Containing Rational Expressions 1. Identify the Least Common Denominator (LCD) of all the fractions . In some instances you may need to factor the denominators first. 2.
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Other-Equations - Other Algebraic Equations Including...

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