Adding, Subtracting, Multiplying and Dividing 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, combined using addition, subtraction, and multiplication.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c). It is a shortcut that uses the coefficients of the polynomial to perform the division more efficiently than long division.

Front

How do you evaluate a polynomial function at a given value?

Back

To evaluate a polynomial function f(x) at a specific value x = a, substitute 'a' for 'x' in the polynomial expression and simplify.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression. It indicates the polynomial's behavior and the number of roots it can have.

Front

What is the quotient in polynomial division?

Back

The quotient in polynomial division is the result obtained when one polynomial is divided by another. It represents how many times the divisor fits into the dividend.

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What is the remainder in polynomial division?

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The remainder in polynomial division is the part of the dividend that is left over after dividing by the divisor. It can be expressed as a polynomial of a lower degree than the divisor.

Front

What is the process of adding polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable parts the same.

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What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. They can be combined by adding or subtracting their coefficients.

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms.