Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, and coefficients. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x^2 is a monomial.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the result of (a + b)^2?

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The result of (a + b)^2 is a^2 + 2ab + b^2.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).

Front

How do you simplify the expression (2x^2 - 4y + 7xy - 6y^2) - (-3x^2 + 5y - 4xy + y^2)?

Back

Combine like terms: 5x^2 - 9y + 11xy - 7y^2.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 2x^2 - x + 7.