Polynomials and Polynomial opperations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 3x^4 + 2x^3 - x + 5.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term (e.g., 3x), a binomial has two terms (e.g., x + 2), and a trinomial has three terms (e.g., x^2 + 3x + 4).

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property or the FOIL method. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is equal to a^2 + 2ab + b^2. For example, (x + 3)^2 = x^2 + 6x + 9.

Front

What is the value of f(2) if f(x) = 2x^2 - 5x?

Back

f(2) = 2(2)^2 - 5(2) = 8 - 10 = -2.

Front

What is the value of f(0) if f(x) = -3x^2 + 5x + 1?

Back

f(0) = -3(0)^2 + 5(0) + 1 = 1.