Add/Subtract 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

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions to form a new polynomial.

Front

What are like terms in polynomials?

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

How do you subtract polynomials?

Back

To subtract polynomials, you distribute the negative sign to the terms of the polynomial being subtracted and then combine like 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 4x^3 - 2x^2 + 7, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent.

Front

What is the result of adding (2x^2 + 3x) and (4x^2 - 5x)?

Back

The result is 6x^2 - 2x.

Front

What is the result of subtracting (3x^3 + 2x) from (5x^3 - 4x)?

Back

The result is 2x^3 - 6x.

Front

What is the simplified form of (x^2 + 2x) + (3x^2 - x)?

Back

The simplified form is 4x^2 + x.