Add/Subtract/Multiply 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 the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 3x^2 + 2x + 1, the degree is 2.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It is used to multiply a single term by a polynomial.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property or FOIL method for binomials. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as x + 3 or 2x^2 - 5.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms, such as x^2 + 2x + 1.

Front

What is the result of multiplying (x - 3)(x^2 + 2x + 7)?

Back

The result is x^3 - x^2 + x - 21.

Front

What is the sum of (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8)?

Back

The sum is 3y^3 + 7y^2 - 4y + 3.