Adding and Subtracting 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. For example, 3x^2 + 2x - 5 is a polynomial.

Front

How do you add polynomials?

Back

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

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x + 4) - (2x + 5) = (3x - 2x) + (4 - 5) = x - 1.

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 degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x, 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 - 2, the leading coefficient is 5.

Front

What is the result of (3x + 4y - 3z) - (2x - 6y + 7z)?

Back

The result is x + 10y - 10z.

Front

What is the result of (5x^4 - 4x^3 - 2x^2 + x - 19) - (x^4 + 5x^3 + 8x^2 + x + 5)?

Back

The result is 4x^4 - 9x^3 - 10x^2 - 24.

Front

What is the result of (2a^2 + 5a + 3) - (a^2 - 3a - 4)?

Back

The result is a^2 + 8a + 7.

Front

What is the result of (−x^4 + 13x^5 + 6x^3) + (6x^3 + 5x^5 + 7x^4)?

Back

The result is 18x^5 + 6x^4 + 12x^3.