Operations with Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 5x^3 - 13x^2 + 24x + 12, the degree is 3.

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms.

Front

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

Back

The result is x^2 + 5x + 6.

Front

How do you simplify the expression (4x^2 + x) - (x^2 + 2x)?

Back

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

Front

What is the formula for the square of a binomial (a - b)^2?

Back

The formula is (a - b)^2 = a^2 - 2ab + b^2.

Front

What is the product of (x - 2)^2?

Back

The product is x^2 - 4x + 4.

Front

How do you add two polynomials?

Back

To add two polynomials, combine like terms by adding the coefficients of the same degree terms.

Front

What is the result of adding the polynomials (-3x + 4) + (8x - 5)?

Back

The result is 5x - 1.

Front

What is a binomial?

Back

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