Adding and Subtracting 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 are the degrees of polynomials?

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

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2+4)x^2 + (3+5)x = 6x^2 + 8x.

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, while 3x^2 and 4x are not.

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x^2 + 2x) - (x^2 + 4x) = (3x^2 - x^2) + (2x - 4x) = 2x^2 - 2x.

Front

What is the result of adding (2x^2 + 5x - 7) and (3 - 4x^2 + 6x)?

Back

The result is -2x^2 + 11x - 4.

Front

What is the result of adding (3y^2 + y^3 - 5) and (4y^2 - 4y + 2y^3 + 8)?

Back

The result is 3y^3 + 7y^2 - 4y + 3.

Front

How do you simplify the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

The simplified expression is 11a^3 - 4a^2 - 14a - 7.

Front

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

Back

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

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.