Polynomials: Naming, Adding, Subtracting & Multiplying

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, along with coefficients. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 - 2x^2 + x - 7.

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) = 7x^2 + 2x + 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 degree of a polynomial?

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 a linear polynomial?

Back

A linear polynomial is a polynomial of degree 1, which can be expressed in the form ax + b, where a and b are constants. For example, 2x + 3.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, expressed in the form ax^2 + bx + c, where a, b, and c are constants. For example, x^2 - 4x + 4.

Front

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

Back

The product is x^3 - x^2 - x + 1.

Front

What is the product of (x + 4)(x - 2)?

Back

The product is x^2 + 2x - 8.

Front

How do you classify polynomials by degree?

Back

Polynomials can be classified as constant (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3), and so on.