Review for Test on Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What are the terms in the polynomial -27a^3 + 9a^2 - 45a?

Back

The terms are -27a^3, 9a^2, and -45a. There are 3 terms in total.

Front

How do you simplify the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

Combine like terms to get 11a^3 - 4a^2 - 14a - 7.

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 exponents.

Front

Which polynomial is in standard form: 9x^3 + 8x^2 - 3x - 11 or -3x + 8x^2 + 9x^3 - 11?

Back

9x^3 + 8x^2 - 3x - 11 is in standard form.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to combine like terms and reduce it to its simplest form.

Front

How do you multiply two binomials, such as (3x + 1)(4x + 2)?

Back

Use the distributive property (FOIL method) to get 12x^2 + 10x + 2.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of its variable.

Front

What is the leading coefficient of the polynomial 9x^3 + 8x^2 - 3x - 11?

Back

The leading coefficient is 9, which is the coefficient of the term with the highest degree.

Front

How do you factor the expression 3ab(a^2b + ab^3)?

Back

Distribute to get 3a^3b^2 + 3a^2b^4.