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Intermediate Algebra II Section 5-4 (3 days/1 sheet) Template I. Objective: To divide polynomials using long & synthetic division. II. Teacher activities: A. Compare polynomial division to long division: 658 ÷ 31 (6 x2 5x 8) (3x 1) Rules for dividing polynomials by binomials: 1) Check for standard form 2) Check for missing terms – replace w/ 0 as the coefficient 3) Divide as if numbers 4) Place like terms over reach other 5) Write remainder over divisor & add to quotient Use Polynomial long division. Is x – 1 a factor of 6 x 2 11x 5 ? 6 x 2 11x 5 Ex 1 x 1 Day 2: Synthetic Division – an efficient way to divide a polynomial by a linear binomial in the form x – a 1. Check for standard form & missing terms 2. Write the coefficients with a in front (opposite of constant of divisor) 3. Bring lead coefficient down then multiply & add Ex 2 Use synthetic division (2 x3 10 x2 9 x 15) ( x 3) x3 1 Ex 3 Use synthetic division x 1 Day 3: Remainder Theorem – If P(x) is divided by x – a, P(a) is the remainder. Ex 4 Use synthetic division/ Substitution & the Remainder Theorem to find P(a). P( x) x5 2 x3 x2 2, a 3 III. Assignment: Day 1, p321: 5-15odd Day 2, p325: 7-15all Day 3: p325: 16-29all, omit 20 Review packet over 5.1-5.4