Daily Warm-UP Quiz
Factor completely:
1. x4 – 17x2 +72
2. x4 + 12x2 +36
3. x4 – 7x2 +12
4. x8 – 81
5. x6 – 25
6. x6 – 36
Quiz (NO notes!)
1. Write your first ten perfect cubes.
EX. 13 = __ 23= __ 33= __ etc.
2. Given the function f(x) = (x+3)3,
describe the appearance of the graph w/o
actually graphing.
3. Factor completely: x3 + 27
1. Write your first ten perfect cubes.
EX. 13 = __ 23= __ 33= __ etc.
2. (x-5)3 = _______________
3. Factor completely:
x3 -125 -15x2 +75x
4. Divide using long division:
÷ x -5
5. x3 – 53 = ________________________
Dividing Polynomials
At the end of this
two-part lesson, you
should be able to:
 Divide polynomials
using long division
 Divide polynomials
using synthetic
division
PART I: DIVIDING POLYNOMIALS
USING LONG DIVISION
Divide:
Check Your Answer Using
Multiplication:
(x-3) (x3 + 3x2 + 9x + 27) =
Check your answer here!
Checking for Understanding
Divide 2x4 + 4x3 - 5x2 + 2x – 3 by x2 + 2x + 3
Check:
Determining Polynomial
Factors
You can use long
division to
determine the
factors of a
polynomial!
ALERT!
Determine whether each divisor is a
factor of each dividend. Explain.
(5x4 + 18x3 + 10x2 + 3x) (x3 + 6x2 - 5x + 20)
x2 + 3x
x2 + 5
Daily Warm-UP Quiz
1. Factor completely:
a. x3 – 27
b. x3 + 64
2. Multiply:
a. (x + 3)3
b. (x -2) 3
3. Simplify:
a. √-25 b. √-50
c. √-16
e. -8 +/- √-48
16
f. -15 +/- √-50
30
d. √-48
Honors
Algebra 2
is child’s
play
compared
to this
workout!
PART II: DIVIDING POLYNOMIALS
USING SYNTHETIC DIVISION
When a divisor is
of the form
x  c where c
_______,
is a constant,
synthetic
division
_____________
can be used.
ALERT!
Synthetic Division
Divide using synthetic division:
(x 3 + 2x2 - 4x + 8) ÷ (x + 2)
Step 1: Check to determine that the
divisor is of the form x + c or x – c.
Step 2: Determine the zero, based
upon the divisor, to set up the problem
using synthetic division.
Synthetic Division
-2
1
2
-4
8
To check your answer,
multiply the quotient by the divisor
and add the remainder. It
should be the same as theRemainder
original
polynomial.
Zero
Divide using synthetic division:
REMAINDER
THEOREM
If a polynomial f(x) is
divided by (x - k), the
remainder is r = f(k).
Without dividing, determine
the remainder of
(x 3 + 2x 2 - 4x + 8) ÷ (x + 2)
FACTOR
A polynomial, f(x) has a factor
THEOREM (x- k) if and only if f(k) = 0.
Determine if x + 2 is a
factor of
(x 3 + 2x 2 - 4x + 8)
Final Checks for Understanding
1.
2.
3.
4.
5.
Given that f(x) = 2x3 + 11x2 + 18x + 9 has
x = -3 as a zero, factor f(x).
What kind of divisor is required for
synthetic division?
Evaluate f(x) = 2x3 + 6x2 – 8 at x = 1.
Factor 2x3 + 6x2 – 8 completely.
Write the polynomial divisor, dividend, and
quotient that the synthetic division below
represents:
1
2 6 0 -8
2 8 8
2 8 8 0
Homework
PART I: DIVIDING POLYNOMIALS
USING LONG DIVISION
Divide
X-3
(-)
(-)
(-)
(-)
x3 + 3x2 + 9x + 27x
x4 -0x3 + 0x2 + 0x1 -81
x4 - 3x3
3x3 + 0x2
3x3 - 9x2
9x2 + 0x1
9x2 – 27x1
27x1 -81
27x1 -81
Return to lesson!