Polynomials Flashcards

1
Q

What is a polynomial?

A

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.

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2
Q

True or False: A polynomial can have negative exponents.

A

False

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3
Q

What is the degree of the polynomial 4x^3 + 2x^2 - x + 7?

A

3

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4
Q

Fill in the blank: The polynomial 5x^4 - 3x^2 + 2 can be classified as a ______ polynomial.

A

quartic

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5
Q

What is the leading coefficient of the polynomial 6x^5 - 4x^3 + x?

A

6

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6
Q

Which of the following is a polynomial: 3x^2 + 2x - 5, 1/x + 2, or sqrt(x)?

A

3x^2 + 2x - 5

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7
Q

True or False: The expression x^2 + 2x + 1 can be factored as (x + 1)(x + 1).

A

True

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8
Q

What is the sum of the polynomials (2x^2 + 3x) and (4x^2 - x + 1)?

A

6x^2 + 2x + 1

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9
Q

Which term is the constant term in the polynomial 7x^3 + 4x^2 - 2x + 5?

A

5

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10
Q

Fill in the blank: The polynomial expression 2x^3 - 3x + 1 is of degree ______.

A

3

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11
Q

What is the product of the polynomials (x + 2) and (x - 3)?

A

x^2 - x - 6

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12
Q

True or False: The polynomial x^4 - 5x^2 + 6 can be factored into linear factors.

A

False

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13
Q

What is the difference of the polynomials (3x^3 + 2x) and (x^3 - 4x)?

A

2x^3 + 6x

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14
Q

What is the value of the polynomial 2x^2 - 3x + 4 when x = 2?

A

6

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15
Q

Fill in the blank: A polynomial with one term is called a ______ polynomial.

A

monomial

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16
Q

What is the result of dividing the polynomial 4x^4 by 2x^2?

A

2x^2

17
Q

Which of the following is the correct factorization of x^2 - 9?

A

(x - 3)(x + 3)

18
Q

True or False: The polynomial 5x^3 + 4x^2 - x + 10 is a cubic polynomial.

A

True

19
Q

What is the remainder when the polynomial 3x^3 + 2x^2 - x + 5 is divided by x - 1?

A

9

20
Q

Fill in the blank: The polynomial 4x^2 + 7x + 10 can be classified as a ______ polynomial.

A

quadratic

21
Q

What is the zero of the polynomial x^2 - 4?

A

x = 2 or x = -2

22
Q

What is the leading term of the polynomial 9x^5 - 3x^4 + 2x?

A

9x^5

23
Q

True or False: The polynomial 3x^2 - 2x + 1 has a maximum value.

A

False

24
Q

What is the result of evaluating the polynomial 2x^2 + 3 at x = -1?

A

5

25
Q

Fill in the blank: The polynomial x^3 + 2x^2 + x can be expressed as ______.

A

x(x^2 + 2x + 1)