Warm Up

P 112 # 1-8 (not the vocabulary)

Math IV Lesson 9 Real Zeros of polynomial functionsEssential 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) whenF(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