Adding, Subtracting, Multiplying, and Dividing 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

How do you classify polynomials by degree?

Back

Polynomials are classified by their degree, which is the highest power of the variable in the expression. For example, a polynomial of degree 2 is called quadratic, degree 3 is cubic, degree 4 is quartic, and so on.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term (e.g., 3x), a binomial has two terms (e.g., x + 2), and a trinomial has three terms (e.g., x^2 + 3x + 4).

Front

What is the product of (a + b)(a - b)?

Back

The product is a^2 - b^2, which is known as the difference of squares.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 5.

Front

What is the result of subtracting polynomials?

Back

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

Front

What is the formula for multiplying two binomials?

Back

The formula is (a + b)(c + d) = ac + ad + bc + bd. This is also known as the FOIL method (First, Outside, Inside, Last).

Front

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

Back

Distribute 3x to both terms: 3x * 2x + 3x * 4 = 6x^2 + 12x.

Front

What is the degree of the polynomial 4m^2 + 9?

Back

The degree is 2, making it a quadratic polynomial.

Front

What is the sum of the polynomials (2x^2 + 3x) and (4x^2 + 5)?

Back

The sum is (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.