Polynomial Operations

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, 2x^2 + 3x + 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What is a like term?

Back

Like terms are terms in a polynomial 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 second polynomial 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 polynomial. For example, in 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, the leading coefficient is 5.

Front

What is the sum of (5x + 2) + (4x + 5)?

Back

The sum is 9x + 7.

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 sum of (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8)?

Back

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

Front

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

Back

The result is 2x^2 + x - 10.