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 + 1 is a polynomial.

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 the polynomial 4x^3 + 2x^2 + 5, the degree is 3.

Front

How do you subtract polynomials?

Back

To subtract polynomials, you subtract the coefficients of like terms. For example, (3x^2 + 2x) - (x^2 + 4x) = (3x^2 - x^2) + (2x - 4x) = 2x^2 - 2x.

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

Front

What is the result of subtracting (2x + 5y) - (3x - 2y)?

Back

The result is -x + 7y.

Front

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

Back

The result is -x^2 - 6x + 8.

Front

What is the result of subtracting (x^5 + x^3) - (6x - x^3 + 6x^5)?

Back

The result is -5x^5 + 2x^3 - 6x.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in the term 4x^2, 4 is the coefficient.

Front

What is a constant term in a polynomial?

Back

A constant term is a term in a polynomial that does not contain any variables. For example, in the polynomial 3x^2 + 2x + 5, the constant term is 5.

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^3 + 2x^2 + x + 5 is in standard form.