Synthetic division

Warm Up
P 112 # 1-8 (not the vocabulary)
Math IV Lesson 9 Real
Zeros of polynomial
Essential Question: How do you divide a
polynomial by another polynomial?
Standard: MM4A4. Students will investigate
a. Compare and contrast properties of functions
within and across the following types: linear,
quadratic, polynomial, power, rational,
exponential, logarithmic, trigonometric, and
 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
 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
 Page
127 # 1-4, 15-18, 35
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