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Cubic, Square Root and Rational Functions

Cubic, Square Root and Rational Functions. Factor Cubics. Radical Expressions & Equations. Rational Expressions & Equations. How do we factor cubics?. How do we simplify radical expressions?. How do we add, subtract, multiply, divide and simplify rational expressions?.

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Cubic, Square Root and Rational Functions

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  1. Cubic, Square Root and Rational Functions Factor Cubics Radical Expressions & Equations Rational Expressions & Equations How do we factor cubics? How do we simplify radical expressions? How do we add, subtract, multiply, divide and simplify rational expressions? Product Property of Radicals: Quotient Property of Radicals: Radical Conjugates: Special Product Patterns: (x + y)3 = x3 + 3x2y + 3xy2 + y2 (x − y)3 = x3 − 3x2y + 3xy2 − y2 Factor Out a Monomial GCF: 2x3 − 6x2y + 6xy2 − 2y2 = 2(x3 − 3x2y + 3xy2 − y2) =2(x – y)3 Multiple Variables: a3b3 + 12a2b2 + 4ab +64 = (ab + 4)3 • Rational expressions arethe ratio of 2 polynomials. • Add, subtract, multiply & divide as for any fractions. • Then, factor (if needed) & simplify. • Check for excluded values. How do we solve rational equations? How do we solve radical equations? • Use the Cross ProductsProperty to solve as for aproportion. • Multiply by the LCD to eliminate denominators. • Isolate radical. • Square both sides. • Simplify and solve. • Check for extraneous solutions. FACTOR: SIMPLIFY: SOLVE: SIMPLIFY: SOLVE: 8x3 + 12x2y +6xy2 + y3

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