Operations with Polynomials Test 2024

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 is the degree of the polynomial 3x^2 + 2x + 1?

Back

The degree of the polynomial 3x^2 + 2x + 1 is 2, which is the highest exponent of the variable x.

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms.

Front

What is the result of multiplying (x^2 - 2x + 1)(x + 1)?

Back

The result is x^3 - x^2 - x + 1.

Front

What is the sum of the polynomials (2x + 5y) and (3x - 2y)?

Back

The sum is 5x + 3y.

Front

What is the process for simplifying a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator, cancel any common factors, and rewrite the expression.

Front

What is the simplified form of (6a^3b^2c^4 - 8a^2b^2c) / (2a^2bc)?

Back

The simplified form is 3abc^3 - 4b.

Front

What is the leading coefficient of the polynomial 4x^3 - 2x^2 + 5?

Back

The leading coefficient is 4, which is the coefficient of the term with the highest degree.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms.

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, from highest to lowest.