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

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves taking the difference of like terms from two polynomial expressions. For example, (3x^2 + 4x) - (x^2 + 2) = 2x^2 + 4x + 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. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

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

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.

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What is the result of (x - 1)(x - 8)?

Back

The result is x^2 - 9x + 8.

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What is the result of (x - 3)(x + 10)?

Back

The result is x^2 + 7x - 30.

Front

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

Back

The result is 4x^2 + 11x + 6.

Front

How do you find the sum of two polynomials?

Back

To find the sum, combine like terms from both polynomials. For example, (2x^2 + 5x - 7) + (3 - 4x^2 + 6x) = -2x^2 + 11x - 4.