Operations with 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 is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

How do you simplify the expression -3n^3 + 8n - 6n^3?

Back

Combine like terms: -3n^3 - 6n^3 + 8n = -9n^3 + 8n.

Front

What is the result of (5x + x^3) - (2x^2 + 3x)?

Back

x^3 - 2x^2 + 2x.

Front

What is the product of (4x + 2)(2x - 2)?

Back

8x^2 - 4x - 4.

Front

What is the result of (4x - 1)(3x^2 - 2x + 5)?

Back

12x^3 - 11x^2 + 22x - 5.

Front

What does it mean to combine like terms in a polynomial?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

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 when the terms are arranged in descending order of their degrees.

Front

How do you factor the polynomial x^2 - 5x + 6?

Back

The factors are (x - 2)(x - 3).