Adding, Subtracting, & Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

How do you determine the number of terms in a polynomial?

Back

Count the distinct terms in the polynomial. For example, in 3x^3 - 2x + 8x - 16, the terms are 3x^3, 6x, and -16, totaling 3 terms.

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 x^4 - 9x + 1, the degree is 4.

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^2 - 6x - 13.

Front

How do you add polynomials?

Back

Combine like terms by adding their coefficients. For example, (3x^3 + 3x^2 - 4x + 5) + (x^3 - 2x^2 + x - 4) results in 4x^3 + 1x^2 - 3x + 1.

Front

How do you subtract polynomials?

Back

Distribute the negative sign and then combine like terms. For example, (4x^2 + x) - (x^2 + 2x) results in 3x^2 - x.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and -5x^2 are like terms.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 5x^2, 5 is the coefficient.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial. For example, in 4x^3 + 2x^2 - 5, the leading coefficient is 4.

Front

What is the constant term in a polynomial?

Back

The constant term is the term in a polynomial that does not contain any variables. For example, in 3x^2 - 4x + 7, the constant term is 7.