Understanding Polynomials

What is a polynomial?

• A polynomial is an equation with only one variable.

• A polynomial is an expression of the form a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.

• A polynomial is a single number.

• A polynomial is a type of geometric shape.

Identify the degree of the polynomial 3x^4 + 2x^2 - x + 5.

• 4

• 5

• 3

• 2

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

• 3

• 7

• 2

• -4

How do you add the polynomials (2x^2 + 3x) and (4x^2 - x + 1)?

• 4x^2 + 3x + 2

• 6x^2 + 2x + 1

• 6x^2 - 3x + 1

• 2x^2 + 4x + 1

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

• x^2 + 5x - 6

• x^2 - 5

• x^2 - x - 6

• x^2 + x + 6

Define a monomial and give an example.

• x^3 - 4x

• 7y + 5z

• 5x^2

• 3x + 2

What is the difference between a polynomial and a rational function?

• A polynomial is a single expression of variables and constants, while a rational function is a ratio of two polynomials.

• A polynomial can only have positive exponents, while a rational function can have negative exponents.

• A polynomial is a function defined only for integers, while a rational function can be defined for all real numbers.

• A polynomial is always a linear function, while a rational function can be nonlinear.

How do you factor the polynomial x^2 - 9?

• (x - 9)(x + 1)

• (x - 3)(x - 3)

• (x - 3)(x + 3)

• (x - 4)(x + 4)

What is the value of the polynomial 2x^2 + 3x - 5 when x = 2?

• 7

• 11

• 4

• 9

Explain the Remainder Theorem in relation to polynomials.

• The Remainder Theorem indicates that the remainder is always zero when dividing by (x - c).

• The Remainder Theorem applies only to linear equations and not to polynomials.

• The Remainder Theorem states that f(c) is the quotient when f(x) is divided by (x - c).

• The Remainder Theorem states that f(c) is the remainder when f(x) is divided by (x - c).