4.4(B) Practice - Alg2 - Fall 24

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What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

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How do you determine if (x - c) is a factor of a polynomial?

Back

To determine if (x - c) is a factor of a polynomial f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

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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 faster than long division and involves using coefficients.

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What is the process for polynomial long division?

Back

Polynomial long division involves dividing the leading term of the dividend by the leading term of the divisor, multiplying the entire divisor by that result, subtracting from the dividend, and repeating the process.

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What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial and determines the polynomial's end behavior and the number of possible roots.

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

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What does it mean for a polynomial to be factored completely?

Back

A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the given number system.

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What is the difference between a factor and a multiple?

Back

A factor of a number or polynomial divides it evenly, while a multiple is the result of multiplying that number or polynomial by an integer.

Front

What is the role of coefficients in a polynomial?

Back

Coefficients are the numerical factors that multiply the variable terms in a polynomial, determining the polynomial's shape and behavior.

Front

What is the purpose of finding the remainder when dividing polynomials?

Back

Finding the remainder helps in understanding the behavior of the polynomial, particularly in relation to its roots and factors.