Polynomials Flashcards
What is a polynomial?
A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.
True or False: A polynomial can have negative exponents.
False
What is the degree of the polynomial 4x^3 + 2x^2 - x + 7?
3
Fill in the blank: The polynomial 5x^4 - 3x^2 + 2 can be classified as a ______ polynomial.
quartic
What is the leading coefficient of the polynomial 6x^5 - 4x^3 + x?
6
Which of the following is a polynomial: 3x^2 + 2x - 5, 1/x + 2, or sqrt(x)?
3x^2 + 2x - 5
True or False: The expression x^2 + 2x + 1 can be factored as (x + 1)(x + 1).
True
What is the sum of the polynomials (2x^2 + 3x) and (4x^2 - x + 1)?
6x^2 + 2x + 1
Which term is the constant term in the polynomial 7x^3 + 4x^2 - 2x + 5?
5
Fill in the blank: The polynomial expression 2x^3 - 3x + 1 is of degree ______.
3
What is the product of the polynomials (x + 2) and (x - 3)?
x^2 - x - 6
True or False: The polynomial x^4 - 5x^2 + 6 can be factored into linear factors.
False
What is the difference of the polynomials (3x^3 + 2x) and (x^3 - 4x)?
2x^3 + 6x
What is the value of the polynomial 2x^2 - 3x + 4 when x = 2?
6
Fill in the blank: A polynomial with one term is called a ______ polynomial.
monomial
What is the result of dividing the polynomial 4x^4 by 2x^2?
2x^2
Which of the following is the correct factorization of x^2 - 9?
(x - 3)(x + 3)
True or False: The polynomial 5x^3 + 4x^2 - x + 10 is a cubic polynomial.
True
What is the remainder when the polynomial 3x^3 + 2x^2 - x + 5 is divided by x - 1?
9
Fill in the blank: The polynomial 4x^2 + 7x + 10 can be classified as a ______ polynomial.
quadratic
What is the zero of the polynomial x^2 - 4?
x = 2 or x = -2
What is the leading term of the polynomial 9x^5 - 3x^4 + 2x?
9x^5
True or False: The polynomial 3x^2 - 2x + 1 has a maximum value.
False
What is the result of evaluating the polynomial 2x^2 + 3 at x = -1?
5
Fill in the blank: The polynomial x^3 + 2x^2 + x can be expressed as ______.
x(x^2 + 2x + 1)
