Operations with Polynomials

Front

What is a polynomial?

Back

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

Front

How do you classify a polynomial by degree?

Back

Polynomials are classified by their degree: 0 (constant), 1 (linear), 2 (quadratic), 3 (cubic), and so on.

Front

What is a quadratic trinomial?

Back

A quadratic trinomial is a polynomial of degree 2 that has three terms, typically in the form ax² + bx + c.

Front

What is the degree of the polynomial 12?

Back

The degree of the polynomial 12 is 0, making it a constant polynomial.

Front

What is the degree of the polynomial 2x - 9?

Back

The degree of the polynomial 2x - 9 is 1, making it a linear polynomial.

Front

How do you simplify the expression -3x²(7x² - x + 4)?

Back

To simplify, distribute -3x²: -3x² * 7x² = -21x⁴, -3x² * -x = 3x³, -3x² * 4 = -12x². The simplified expression is -21x⁴ + 3x³ - 12x².

Front

What is the result of multiplying (4x + 1)(5x - 2)?

Back

The result of multiplying (4x + 1)(5x - 2) is 20x² - 3x - 2.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of degrees, from the highest degree term to the lowest.

Front

What are the coefficients in a polynomial?

Back

Coefficients are the numerical factors in front of the variables in a polynomial.

Front

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

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms.