Long

1
Rational Zeros Theorem
Upper Lower Bounds
Long Division
RemainderTheorem
Factor Theorem
Synthetic Division
100
100
100
100
100
100
200
200
200
200
200
200
300
300
300
300
300
300
400
400
400
400
400
400
500
500
500
500
500
500
2
Division involves a dividend divided by a divisor
to obtain a quotient and a _________.
remainder
3
What is the answer of 2x4-x3-2 divided by
2x2x1? Write in polynomial form.
2x4-x3-x(2x2x1)(x2-2)(x-2)
4
Divide f(x)x2-2x3 b x-1. Write in polynomial
form.
f(x)(x1)22
5
Divide f(x)x34x27x-9 by x3 and write a
summary statement in polynomial form.
f(x)(x2x4)(x3)-21
6
Divide f(x)x4-2x33x2-4x6 by x22x-, write a
summary statement in fraction form.
f(x)(x2-4x12)(x22x-1)-32x18
7
If a polynomial is divided by ___, then the
remainder is rf(k).
x-k
8
Using the remainder theorem, find the remainder
when f(x)3x27x-20 is divided by x1.
rf(-1)3(-1)27(-1)-203-7-20-24
9
What is the remainder when f(x)2x2-3x1 is
divided by x-2?
3
10
Use the remainder theorem to find the remainder
when you divide f(x)x3-x22x-1 by x3
-43
11
Use the remainder theorem to find the remainder
when f(x)2x3-3x24x-7 by x-2
5
12
A polynomial function f(x) has a factor x-k if
and only if f(k)_.
0
13
Using the factor theorem, factor f(x)3x27x-20
by dividing it by the known factor x4.
(3x-5)
14
Is x-1 a factor of x3-x2x-1?
Yes
15
Use the factor theorem to determine whether x-2
is a factor of x33x-4
No
16
Use the factor theorem to determine where x2 is
a factor of 4x39x2-3x-10
Yes
17
This shortcut method for the division of a
polynomial by a ______ _______ x-k is synthetic
division.
linear divisor
18
Divide 2x3-3x2-5x-12 by x-3 using synthetic
division and write a summary statement in
fraction form.
2x3-3x2-5x-12 2x23x4 x-3
19
Divide using synthetic division and write a
summary statement in fraction form
x3-5x23x-2x1
X2-6x9 -11 x1
20
Divide using synthetic division and write a
summary statement in fraction form
9x37x2-3xx-10
9x297x967 9670 x-10
21
Divide using synthetic division and write a
summary statement in fraction form 5x4-3x14-x
-5x3-20x2-80x-317 -1269
4-x
22
Real zeros of a polynomial function are either
________ zeros zeroes that are rational numbers
or __________ zeros zeros that are irrational
numbers.
rational, irrational
23
Find the rational zeros of f(x)x3-3x21
f(1)(1)3-3(1)21-1 f(-1)(-1)3-3(-1)21-3 So f
has no rational zeros.
24
Use the rational zeroes theorem to write a list
of all possible rational zeroes of f(x)6x3-5x-1
1 1, 2, 3, 6 (all positive negative)
25
Use the rational zeroes theorem to write a list
of possible rational zeroesf(x)2x3-x2-9x9
1, 3, 9 1, 2 (all positive negative)
26
Find all the zeroes of the function and identify
each zero as rational or irrationalf(x)2x4-7x3-
2x2-7x-4
-1/2 and 4 rational No irrational
27
We narrow our search for real zeros by using a
test that identifies upper and lower ______ for
real zeros.
bounds
28
Find a lower bound of f(x)2x4-7x3-8x214x8
-2
29
Use synthetic division to prove that to number k
is an upper bound for the real zeroes of the
functionk3 f(x)2x3-4x2x3
Yes
30
Use synthetic division to prove that the number k
is an upper bound for the real zeroes of the
function fk2 f(x)x4-x3x2x-12
Yes
31
Use synthetic division to prove that the number k
is a lower bound for the real zeroes of the
function fk-1 f(x)3x2-4x2x-2
Yes