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, 4x^3 + 3x^2 - 2x + 1 is a polynomial.

Front

What does it mean to combine like terms in a polynomial?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power. For example, in the expression 3x + 4x, you can combine the like terms to get 7x.

Front

How do you add two polynomials?

Back

To add two polynomials, combine like terms by adding the coefficients of terms with the same degree. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

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

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 7x^3, 7 is the coefficient.

Front

What is the result of adding (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

The result is 11x^4 + 2x^2 + 14x.

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What is the result of adding (3x^2 + xy - 5y^2) + (2x^2 - xy + 3y^2)?

Back

The result is 5x^2 - 2y^2.

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

Back

The result is 3x^3 + 5.

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What is the result of combining like terms in (5x + 2) + (4x + 5)?

Back

The result is 9x + 7.

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What is the result of adding (5x - y) + (2x + 6y)?

Back

The result is 7x + 5y.