Quiz about Math 10-HM Long Test review - Polynomials

Question 1

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4

Accepted Answer

7

Answer

4

Answer

2

Answer

11

Question 2

How many real zeros does the polynomial function
P(x) = x³+2x²+9x+18 have?

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 3

Question 3.

Accepted Answer

2x² + 3x + 8 + (7/x-4)

Answer

2x³ + 3x + (7/x-4)

Answer

2x² + 3x + 8

Answer

2x² - x + 10 + (6/x-4)

Question 4

Question 4.

Accepted Answer

x² + 14x + 48

Answer

x² + 14x + 8 - (4/x + 2)

Answer

x³ + 8 - (4x/x-2)

Answer

x² + 8x + 48

Question 5

Is this division problem worked correctly?

Accepted Answer

This is incorrect!

Answer

This is correct!

Question 6

Question 6.

Accepted Answer

2x² - x + 1 + 9/(x-2)

Answer

2x³ - x² + x + 9

Answer

2x² - x + 10

Answer

x² - 2x + 1

Question 7

The area of a rectangular pool table is: x² + 14x +40.
The length is x+4. What is the width?

Accepted Answer

(x + 10)

Answer

(x + 8)

Answer

(x + 14)

Answer

(x +4)

Question 8

Question 8.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 9

Question 9.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 10

Divide (x³+3x²-4x-12) by (x²+x-6)

Accepted Answer

x+2

Answer

x-2

Answer

x5+6

Answer

x2+2

Question 11

Divide (x² + 5x - 8) by (x + 3). What is the remainder?

Accepted Answer

-14

Answer

16

Answer

12

Answer

-16

Question 12

Find the quotient when (21x²- 52x + 32) is divided by (7x - 8).

Accepted Answer

(3x - 4)

Answer

(3x + 4)

Answer

(3x + 3)

Answer

(3x + 2)

Question 13

Question 13.

Accepted Answer

Quotient: 2x - 3, Remainder: 15

Answer

Quotient: 2x - 3, Remainder: 9

Answer

Quotient: 2x - 5/3, Remainder 0

Answer

Quotient: 2x² - 3x + 15, Remainder 0

Question 14

What is the proper way to write the answer for the following problem?

Accepted Answer

2x³-x²-25x-12

Answer

2x⁴-x³-25x²-12x+0

Question 15

Decide if (x-3) is a factor of 3x³+10x²-x-12

Accepted Answer

No, it is not a factor!

Answer

Yes, it is a factor!

Question 16

Is (x-7) a factor of (x²-5x+14)?

Accepted Answer

No

Answer

Yes

Question 17

What is the remainder when a³ - 4 is divided by a+2?

Accepted Answer

-12

Answer

-2

Answer

-6

Answer

0

Question 18

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

Accepted Answer

Yes, (x-2) is a factor. The remainder is zero.

Answer

Yes, (x-2) is a factor. There is a remainder.

Answer

No, (x-2) is  not a factor. The remainder is zero.

Answer

No, (x-2) is  not a factor. There is a remainder.

Question 19

If x - 2 is NOT a factor of (2x³ - 5x - 7), what is the remainder?

Accepted Answer

-1/x-2

Answer

-13

Answer

2x³ + 4x² +3x - 1

Answer

13/x-2

Question 20

Find all the factors of x³ -3x² -4x +12 given that -2 is a zero.

Accepted Answer

(x-2) (x+2) (x-3)

Answer

(x-2) (x+2) (x+3)

Answer

(x-2) (x-2) (x+3)

Answer

(x+2) (x+2) (x+3)

Question 21

Find all the real zeros of the function
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

Accepted Answer

x = 4, -1/2, 6

Answer

x = 1/2, -6

Answer

x = -1/2, 6

Answer

x = -4, 1/2, -6

Question 22

Is (x-4) a factor of (x³ +x² -16x-16)?

Accepted Answer

YES

Answer

NO

Question 23

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

Accepted Answer

No

Answer

Yes

Question 24

What is the remainder when a³ - 4 is divided by a+2?

Accepted Answer

-12

Answer

-2

Answer

-6

Answer

0

Question 25

Use synthetic division to determine f(-3), if
f(x)= (3x³ -5x² -4x +1).

Accepted Answer

-113

Answer

-25

Answer

25

Answer

113

Question 26

Question 26.

Accepted Answer

x + 5

Answer

x + 5 + (2/2x - 4)

Answer

x - 8

Answer

x - 5 + (3/2x - 4)

Question 27

List all the possible rational zeros
h(x) = x³- 5x²+2x+12

Accepted Answer

1,2,3,4,6,12,-1,-2,-3,-4,-6,-12

Answer

1,2,3,4,6,12

Answer

1,2,6,12

Question 28

List all possible rational zeros
f(x) = 3x⁵-5x²+x+6

Accepted Answer

1/3,2/3,1,2,3,6,-1/3,-2/3,-1,-2,-3,-6

Answer

1, 2, 3, 6, -1, -2, -3, -6

Answer

1/3,2/3,1,2,3,6

Question 29

List all of the possible rational zeros
p(x) = 3x²+x+7

Accepted Answer

-1/3, -7/3, -1, -7, 1/3,7/3,1,7

Answer

1/3,7/3,1,7

Answer

1, 7, 14, 21

Question 30

The largest exponent determines the degree of the polynomial.

Accepted Answer

True

Answer

False

Question 31

The degree of the polynomial determines the number of roots.

Accepted Answer

True

Answer

False

Question 32

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 33

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

Accepted Answer

True

Answer

False

Question 34

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 35

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 36

All imaginary roots comes in pairs.

Accepted Answer

True

Answer

False

Question 37

Find all the roots of y=x³-2x²+4x-8

Accepted Answer

2, 2i, -2i

Answer

-2, 2i, -2i

Answer

2,-2, 2i

Answer

1, 2i, 4

Question 38

What is the Rational Root Theorem?

Accepted Answer

Making a list of p/q will produce a list of possible rational zeros

Answer

The degree of the polynomial determines what the x value will be

Answer

The degree of the polynomial tells us how many solutions the polynomial will have.

Answer

States that a complex number and its conjugate are solutions

Question 39

Use the Rational Root Theorem to list the possible rational zeros.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 40

Use the Rational Root Theorem to list the possible rational zeros.

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 41

Use Descartes Rule of Signs to determine the possible number of positive and negative roots.

Accepted Answer

1 positive, 1 negative

Answer

1 positive, 2 or 0 negative

Answer

0 positive, 1 negative

Answer

What?

Question 42

Use Descartes Rule of Signs to determine the possible number of positive and negative roots.

Accepted Answer

4, 2, or 0 positive roots and 0 negative roots

Answer

3 or 1 positive roots and 0 negative roots

Answer

4, 2, or 0 positive roots and 1 negative root

Answer

What?

Question 43

Use the rational root theorem to state ALL possible roots

Accepted Answer

Plus or Minus:5, 1, 1/2, and 5/2

Answer

Plus or Minus: 5, 1 and 1/2

Answer

Only positive: 5 and 1

Answer

Only negative: 5, 1, 1/2, and 5/2

Question 44

Use the rational root theorem to state all possible roots

Accepted Answer

Plus and Minus:1,1/2, 1/5, 1/10, 2, 2/5, 3, 3/2, 3/5, 3/10, 6, and 6/5

Answer

Only positive: Don't pick this, u should know its plus and minus by now

Answer

Only negative: see option 2

Answer

Plus and Minus: 1, 1/2, 1/5, 1/10, 2, 2/5, 3, 3/2, 3/10, and 6

Question 45

What are the roots of the equation x⁴ - 4x³ - 49x² - 104x - 60 = 0

Accepted Answer

-3, -2, -1, 10

Answer

-10, 1, 2, 3

Answer

1, -2, 3, 10

Answer

-1, 2, -3, 10

Question 46

Solve the equation x⁵ + 3x³ - 4x = 0

Accepted Answer

-1, 0, 1, -2i, 2i

Answer

-2, 0, 2, -i, i

Answer

-1, 0, 1, -i, i

Answer

-2, 0, 2, -2i, 2i

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