Add/Subtract/Multiply Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication. Example: 2x^2 + 3x - 5.

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What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. Example: (2x^2 + 3x) + (4x^2 + 2) = 6x^2 + 3x + 2.

Front

What does it mean to subtract polynomials?

Back

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

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in one polynomial by each term in the other. Example: (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is a like term?

Back

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

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. Example: In 4x^3 + 2x^2 - x, the degree is 3.

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

Front

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

Back

The result is 7x^2 + 2x - 5.

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

Back

The result is 3x^2 - 7.

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What is the result of (x + 1)(x + 2)?

Back

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