Multiplying and Dividing Polynomials Honors Algebra II with Trigonometry Mr. Agnew

Essential Question Essential Vocabulary How do you multiply and divide polynomials? How do you know if a polynomial will have a remainder? Essential Vocabulary Like Terms Synthetic Division Remainder Theorem

Multiplying Polynomials Multiply each term of one polynomial by each term in the other polynomial. Remember when multiplying variables with exponents, add the exponents. Example: 𝑥 4 ∙ 𝑥 3 = 𝑥 7 MULTIPLICATION Examples

Dividing Polynomials DIVISION Long division of polynomials is like long division of numbers. If a binomial goes into polynomial evenly (remainder of 0), then the binomial is a factor of the polynomial. DIVISION

Synthetic Division Synthetic division is a simplified method for dividing polynomials and uses only the coefficients of the polynomial. We can use synthetic division to find all zeros/factors of a polynomial. Examples

Remainder Theorem If a polynomial P(x) of degree n is divided by (x – a), then the remainder is P(a). In other words, when you plug a value into the polynomial, the solution is the remainder of the polynomial. How is this theorem helpful for us? Examples

Homework 6.2: Multiplying and Dividing Polynomials