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Warm Up P 112 # 1-8 (not the vocabulary) Math IV Lesson 9 Real Zeros of polynomial functions Essential Question: How do you divide a polynomial by another polynomial? Standard: MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. NEW VOCABULARY Improper fraction: a fraction in which the numerator is larger than the denominator Proper fraction: a fraction in which the numerator is less than the denominator. Long division: a process for dividing polynomials Synthetic division: the shorter process for dividing polynomials when the polynomial you are dividing by has the form x + a. Long division • Divide 6x3 -19x2 + 16 x – 4 by x – 2 And use the result to factor the polynomial completely. Synthetic division • Use synthetic division to divide x4 -10x2 -2x + 4 by x + 3 The Remainder theorem If a polynomial f(x) is divided by x – k, the remainder is r = f(k) The remainder theorem Use synthetic division to find f(-2) when F(x) = 3x3 + 8x2 +5x – 7 The factor theorem A polynomial f(x) has a factor (x – k) if and only if f(k) = 0 Homework Page 127 # 1-4, 15-18, 35