WorksheetsPolynomial Review
Total questions: 30
Worksheet time: 2hrs 32mins
Name
Class
Date
1.
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
2.
Is (x-2) a factor of f(x)= x3-8x2+14x-4?
a)
Yes, (x-2) is a factor. There is a remainder.
b)
No, (x-2) is not a factor. The remainder is zero.
c)
Yes, (x-2) is a factor. The remainder is zero.
d)
No, (x-2) is not a factor. There is a remainder.
3.
Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).
(2x³ + 4x² - 5) by (x + 3).
a)
2x² + 2x - 4 R(-12)
b)
2x² - 2x + 6 R(-23)
c)
2x² - 2x + 8 R(-20)
d)
2x² - 4x + 1 R0
4.
What does it mean to be a factor of a number?
a)
Divides evenly with a remainder of zero.
b)
Divides unevenly with a remainder of 1.
5.
If you are missing a term in your polynomials (both dividend and divisor), you must put a zero as a coefficient place holder for that term.
a)
True
b)
False
c)
Only for the dividend
d)
Only for the divisor
6.
If 𝒙2+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?
a)
0
b)
-3
c)
9
d)
5
7.
When p(x) = 9x4- 45x3 + 37x2 + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?
a)
p(2) = 656
b)
p(2) = 652
c)
p(2) = -64
d)
p(2) = -368
8.
Is this division problem worked correctly?
a)
This is correct!
b)
This is incorrect!
9.
(2x3 - 5x2 + 3x + 7) ÷ (x - 2)
a)
2x3 - x2 + x + 9
b)
2x2 - x + 1
c)
2x2 - x + 1 + 9/x-2
d)
2x2 - 9x - 15 - 23/x-2
10.
(2x3 + 5x2 + 9) ÷ (x + 3)
a)
2x2 - x + 3
b)
2x3 - x2 + 3x
c)
2x2 + 11x + 33 + 108/x+3
d)
2x2 - 5x + 12
11.
(3x3 - 2x2 - 7x + 6) ÷ (x + 1)
a)
3x3 - 5x2 - 2x + 8
b)
3x2 + x - 6
c)
3x2 - 5x - 2 + 8/x+1
d)
3x3 + x2 - 6x
12.
if f(x) = x3+8x+24, then find f(-2) using synthetic division.
a)
12
b)
8
c)
0
d)
-6
13.
if f(x) = 3x2 -9x -20, find the value of f(5) using synthetic division.
a)
0
b)
10
c)
15
d)
-7
14.
Is (x-2) a factor of f(x)= x3-8x2+14x-4?
a)
Yes, (x-2) is a factor. There is a remainder.
b)
No, (x-2) is not a factor. The remainder is zero.
c)
Yes, (x-2) is a factor. The remainder is zero.
d)
No, (x-2) is not a factor. There is a remainder.
15.
(2x5+5x4−14x3+17x2−7x−3)÷(x−1) Is x-1 a factor of the polynomial?
a)
Yas
b)
No
16.
a)
y = _(x + 2)(x - 1)2
b)
y = -(x - 2)(x + 1)2
c)
y = (x - 2)(x + 1)2
d)
y = -x3
17.
a)
y = -x4 + 5x3 + 2
b)
y = -x3
c)
y = x3 - 3x - 2
d)
y = -x3 + 3x + 2
18.
What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?
a)
-4, -1, 3
b)
3, -3, 4, 1
c)
4, 1, -3
d)
3, -4, -1, 3
19.
Write a 4th degree polynomial function with:
*a positive leading coefficient
*zeros: 9, 3, -2, 0
*a positive leading coefficient
*zeros: 9, 3, -2, 0
a)
y = x(x - 9)(x - 3)(x + 2)
b)
y = x(x + 9)(x + 3)(x - 2)
c)
y = -x(x - 9)(x - 3)(x + 2)
d)
y = -x(x + 9)(x + 3)(x - 2)
20.
What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x3 - 5x2 + 2x - 10
p(x) = x3 - 5x2 + 2x - 10
a)
0
b)
2x-10
c)
-2x-10
d)
2x+10
21.
What is the proper way to write the answer for the following problem?
a)
2x3-x2-25x-12
b)
2x4-x3-25x2-12x+0
22.
What is the remainder when a3 - 4 is divided by a+2?
a)
-2
b)
-6
c)
-12
d)
0
23.
What is the remainder of (3x3 -5x2 -4x +1) ÷ (x + 3)?
a)
-25
b)
25
c)
113
d)
-113
24.
Which term is missing in this problem?
(2x3 + 5x2 + 9) ÷
(x + 3)
(2x3 + 5x2 + 9) ÷
(x + 3)
a)
x4
b)
x3
c)
x2
d)
x
25.
Factor the Trinomial:
x2 - 8x + 15
x2 - 8x + 15
a)
(x + 5) ( x + 3)
b)
(x - 5) (x - 3)
c)
(x + 15) (x - 1)
d)
(x - 7) (x - 8)
26.
Factor: x2 – 5x – 24
a)
(x - 5)(x + 19)
b)
(x - 8)(x + 3)
c)
(x - 3)(x + 8)
d)
(x - 19)(x + 5)
27.
Factor: x2 + 2x – 3
a)
(x - 2)(x + 1)
b)
(x + 1)(x - 3)
c)
(x + 2)(x - 1)
d)
(x - 1)(x + 3)
28.
Factor
x2 + 12x + 36
x2 + 12x + 36
a)
(x + 6)(x +6)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 6)(x - 6)
29.
Factor
k2 - 2k - 24
k2 - 2k - 24
a)
(k+4)(k+6)
b)
(k+4)(k-6)
c)
(k+6)(k-1)
d)
(k-4)(k+6)
30.
Factor
k2+3x-10
k2+3x-10
a)
(k-2)(k+5)
b)
(k-2)(k-5)
c)
(k+10)(k+4)
d)
(k+2)(k-5)
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