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Today in Pre-Calculus

In today's pre-calculus class, we will cover polynomial long division, specifically for finding real zeros. There will be a new seating chart and notes with a handout. We will also review the quiz and assign homework problems from page 223 (questions 1-6 all).

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Today in Pre-Calculus

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  1. Today in Pre-Calculus • New Seating Chart • Notes: (there is a handout) • Finding Real Zeros using Polynomial Long Division • Go over quiz • Homework

  2. Polynomial Long Division Therefore, 2x3 + 3x2 + 5x + 7 = (2x+1)(x2+x+2)+5

  3. Division Algorithm Let f(x), the dividend, and d(x), the divisor, be polynomials with the degree of f greater than or equal to the degree of d, and d(x) ≠ 0. Then, there are unique polynomials q(x), the quotient, and r(x), the remainder, such that f(x) = d(x)∙q(x) + r(x) Using our example:

  4. Division Algorithm • d(x) divides evenly intof(x) when r(x) = 0 (there is no remainder) • If there is a “missing term” in the dividend, you must put a zero in its place.

  5. Practice Divide f(x) by d(x) and write a summary statement in polynomial form and fraction form. f(x) = 6x3 – 7x + 18 and d(x) =x2 +2x – 2

  6. Practice Polynomial form: 6x3 – 7x + 18 = (x2 + 2x – 2)(6x – 12) + (29x – 6) Fraction Form:

  7. Practice Divide f(x) by d(x) and write a summary statement in polynomial form and fraction form. f(x) = 3x3 + 14x2 – 10x – 12 and d(x) =3x + 2 0

  8. Practice Polynomial form: 3x3 + 14x2 – 10x – 12 = (3x +2)(x2 + 4x – 6) Fraction Form:

  9. Homework • Pg. 223: 1-6all

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