Adding 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, along with coefficients. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of their degrees. For example, 7x^3 - 11x^2 + 8x - 5 is in standard form.

Front

How do you add polynomials?

Back

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

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 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 coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in the term 5x^2, 5 is the coefficient.

Front

Add the polynomials: (2x + 3) + (4x - 5)

Back

6x - 2.

Front

Add the polynomials: (x^2 + 2x + 1) + (3x^2 - x + 4)

Back

4x^2 + x + 5.

Front

What is the result of adding the polynomials: (5x^3 - 2x + 1) + (2x^3 + 3x - 4)?

Back

7x^3 + x - 3.

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What is the sum of the polynomials: (x^2 + 4) + (2x^2 - 3x + 1)?

Back

3x^2 - 3x + 5.