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

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from each polynomial. Like terms are terms that have the same variable raised to the same power.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms.

Front

How do you identify like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, in the expression 3x^2 + 5x - 2x^2, the like terms are 3x^2 and -2x^2.

Front

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

Back

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

Front

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

Back

The result is 3x^2 + 3x.

Front

How do you simplify (x^3 - x^2 + 4) - (3x^3 - 2x^2 + 3)?

Back

The simplification results in -2x^3 + x^2 + 1.

Front

What is the simplified form of (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

The simplified form is -8n^2 - 8n + 3.

Front

What is a 'leading coefficient' in a polynomial?

Back

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

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