CP Parts of a Polynomial/Add & Subtract Polynomials

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What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

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What does it mean to subtract polynomials?

Back

Subtracting polynomials involves taking the difference of like terms from two polynomial expressions. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What are like terms in a polynomial?

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

How do you simplify the expression (3x^4 - 4 - 5x^2) - (1 - x^2 + 2x^3)?

Back

The simplified expression is 3x^4 - 2x^3 - 4x^2 - 5.

Front

What is the constant term in the polynomial x^2 - 2x + 5?

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The constant term is 5.

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How do you simplify the expression (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

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

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What is a trinomial?

Back

A trinomial is a polynomial with three terms. For example, 2x^2 + 3x - 5 is a trinomial.

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 -2x^5 + 3x^4, the leading coefficient is -2.

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What is the degree of a polynomial?

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