Adding/Subtracting Polynomials

Front

What is a polynomial?

Back

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

Front

What does it mean to combine like terms in polynomials?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2+4)x^2 + (3+5)x = 6x^2 + 8x.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x^2 + 2) - (x^2 + 4) = 3x^2 - x^2 + 2 - 4 = 2x^2 - 2.

Front

What is a like term?

Back

Like terms are terms that have the same variable raised to the same power. For example, 5x^2 and 3x^2 are like terms, while 5x^2 and 3x 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 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 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

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

Back

The result is -2x^3 + x^2 + 1.

Front

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

Back

The result is 9x - 3.

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

Back

The result is 11a^3 - 4a^2 - 14a - 7.