Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. Example: 3x^2 + 2x - 5.

Front

What are the degrees of polynomials?

Back

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

Front

What is the product of (a + b)(c + d)?

Back

The product is ac + ad + bc + bd, which is derived from the distributive property.

Front

How do you simplify (x^2 + 3x) + (2x^2 + 4)?

Back

Combine like terms: (1x^2 + 2x^2) + (3x) + (4) = 3x^2 + 3x + 4.

Front

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

Back

The result is x^2 + 3x - 2x - 6 = x^2 + x - 6.

Front

What does it mean to combine like terms?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power. Example: 2x + 3x = 5x.

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. Example: 5x (monomial) vs. 5x + 3 (polynomial).

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in one polynomial by each term in the other.

Front

What is the sum of (2x^2 + 3x) + (4x^2 - x)?

Back

The sum is (2x^2 + 4x^2) + (3x - x) = 6x^2 + 2x.

Front

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

Back

The result is x^2 + 2x + 1, derived from the formula (a + b)^2 = a^2 + 2ab + b^2.