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Polynomials Division Guide: Long Division and Synthetic Division

Learn how to divide polynomials using long division and synthetic division techniques, including dividing a polynomial by a monomial. Master dividing each term of a polynomial by a monomial with detailed examples and step-by-step instructions. Practice problems provided for better understanding.

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Polynomials Division Guide: Long Division and Synthetic Division

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  1. 5.3 Dividing Polynomials Objectives: Divide polynomials using long division Divide polynomials using synthetic division

  2. Dividing a Polynomial by a monomial Divide each term of the polynomial by the monomial. Example:

  3. Dividing Using Long Division (x²-2x-15)(x-5)

  4. Try One (2x³-5x²+4x-4)(x-2)

  5. Remainders (x³-6x²+1)(x+2)

  6. Synthetic Division • Synthetic Division is a way to divide a polynomial by a binomial. Variables are not used, only their coefficients. • The divisor must be in the form x-r (use r) • If the coefficient of x is not 1, you must rewrite it in this form (usually involves division) • Variables must be in descending order with no gaps in exponents.

  7. Example r=-2 To write the answer, start 1 degree less than the polynomial you were dividing into. Answer:

  8. Example When the binomial is not in the form x-r, you may have to divide to get it in that form. The coefficient of x must be 1. Divide both by 2 to get it in the form x-r. r=½ Divide every term by 2.

  9. Continued • Rewritten:

  10. Homework Page 236 16-48 EOE

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