Polynomial Division

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial of the same or lower degree, similar to long division with numbers.

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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).

Front

How do you evaluate a polynomial at a specific value?

Back

To evaluate a polynomial p(x) at a value a, substitute a for x in the polynomial and simplify.

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) using coefficients.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of x for which the polynomial evaluates to zero.

Front

How do you find the remainder when dividing polynomials?

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You can find the remainder by using the Remainder Theorem or by performing polynomial long division.

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What is the quotient in polynomial division?

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The quotient is the result of dividing one polynomial by another, excluding the remainder.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What does it mean for a polynomial to be factored?

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Factoring a polynomial means expressing it as a product of its factors, which can be polynomials of lower degrees.

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree and determines the polynomial's end behavior.