5.3 Dividing Polynomials Objectives: 1.Divide polynomials using long division 2.Divide polynomials using synthetic division.

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Presentation transcript:

5.3 Dividing Polynomials Objectives: 1.Divide polynomials using long division 2.Divide polynomials using synthetic division

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

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

Try One (2x³-5x²+4x-4)  (x-2)

Remainders (x³-6x²+1)  (x+2)

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.

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

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.

Continued Rewritten:

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