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

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. They can be combined by adding or subtracting their coefficients.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent.

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

What is the leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term in the polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term in a sum.

Front

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

Back

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

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 sum of (3 - 2x + 2x^2) + (4x - 5 + 3x^2)?

Back

The sum is 5x^2 + 2x - 2.