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Solving Higher Order Polynomials Unit 6

Solving Higher Order Polynomials Unit 6. Students will solve a variety of equations and inequalities including higher order polynomials. Vocabulary. Prime Factor Polynomial Zero Quadratic Solution Inequality Root Equality x -intercept Synthetic division GCF

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Solving Higher Order Polynomials Unit 6

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  1. Solving Higher Order Polynomials Unit 6 Students will solve a variety of equations and inequalities including higher order polynomials.

  2. Vocabulary Prime Factor Polynomial Zero Quadratic Solution Inequality Root Equality x-intercept Synthetic division GCF Trinomial Binomial Grouping Conjugates i

  3. Difference of Squares Factoring Pattern

  4. Sum or Difference of CubesFactoring Pattern

  5. Perfect Square TrinomialFactoring Pattern

  6. Zero Product Property If then either Allows us to solve factored polynomial equations.

  7. Remainder Theorem If a polynomial f(x) is divided by x-r, then the remainder obtained is a constant and is equal to f(r).

  8. Factor Theorem The binomial x-r is a factor of the polynomial f(x) iff f(r) = 0.

  9. Fundamental Theorem of Algebra and Corollary • Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers. • A polynomial equation of degree n has exactly n roots in the set of complex numbers, including repeated roots.

  10. Complex Conjugates Theorem Let a and b be real numbers, and b 0. If a + bi is a zero of a polynomial function with real coefficients, then a – bi is also a zero of the function.

  11. Rational Root (Zero) Theorem Every rational zero of a polynomial function with integral coefficients is in the form of p/q, a rational number in simplest form, where p is a factor of the constant term and q is a factor of the leading coefficient.

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