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 and coefficients. For example, 4x^3 - 5x^2 + 3x is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What are like terms?

Back

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

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 5x = 8x.

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

Front

What is the perimeter of a rectangle?

Back

The perimeter of a rectangle is the total distance around it, calculated as P = 2(length + width).

Front

How do you find the perimeter of a rectangle with width (2x + 3) and length (2x - 4)?

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P = 2((2x + 3) + (2x - 4)) = 2(4x - 1) = 8x - 2.

Front

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

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The result is x^2 + x + 1.

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What is the process of simplifying an expression?

Back

Simplifying an expression involves combining like terms and performing any operations to reduce it to its simplest form.

Front

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

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