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.

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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.

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What does it mean to subtract polynomials?

Back

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

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What are like terms in polynomials?

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Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

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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.

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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. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

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How do you simplify a polynomial?

Back

To simplify a polynomial, combine like terms and eliminate any unnecessary parentheses. For example, 3x + 2x - 5 simplifies to 5x - 5.

Front

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

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

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

Back

The result is -x^2 - 6x + 8.