Polynomials Vocab/Simplify/Multiply Flashcard-

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 is the degree of a polynomial?

Back

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

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2, the leading coefficient is 5.

Front

How do you multiply two binomials?

Back

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

Front

What is 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, 3x^3 - 2x^2 + x - 5 is in standard form.

Front

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

Back

The product is 4x^2 + 12x + 9.

Front

What is the product of (2n - 4)(n^2 + 6n - 4)?

Back

The product is 2n^3 + 8n^2 - 32n + 16.

Front

How do you identify a trinomial?

Back

A trinomial is a polynomial with three terms. For example, 2x^2 + 3x - 5 is a trinomial.

Front

What is a fifth degree polynomial?

Back

A fifth degree polynomial is a polynomial where the highest exponent of the variable is 5. For example, -2x^5 + 3x^4 + 2x^3 is a fifth degree polynomial.

Front

What does it mean to simplify a polynomial?

Back

To simplify a polynomial means to combine like terms and express it in standard form. For example, 3x^2 + 2x - 5 + 4x^2 simplifies to 7x^2 + 2x - 5.