Add Subtract Multiply 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 - 3x^2 + 6x - 4 is a polynomial.

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 the polynomial 9x^5 + 2x^4 - x^3 + 9x^2 - 2, the degree is 5.

Front

How do you add polynomials?

Back

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

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (4x^3 - 3x^2 + 6x - 4) - (-2x^3 + x^2 - 20) = 4x^3 + 2x^3 - 3x^2 - x^2 + 6x + 20 - 4.

Front

What is a constant term in a polynomial?

Back

A constant term is a term in a polynomial that does not contain any variables. For example, in the polynomial x^2 - 2x + 5, the constant term is 5.

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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, while 3x^2 and 4x are not.

Front

What is the result of multiplying (x + 5)(x + 5)?

Back

The result is x^2 + 10x + 25.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It is used to multiply a single term by a sum.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.

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