2.6 Day #1 Warm-up

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What is polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

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What is a rational zero of a polynomial?

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A rational zero of a polynomial is a solution to the polynomial equation that can be expressed as a fraction of two integers.

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How do you find rational zeros using the Rational Root Theorem?

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The Rational Root Theorem states that any rational solution, expressed as a fraction p/q, has p as a factor of the constant term and q as a factor of the leading coefficient.

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What is the process of synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c).

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What is the first step in polynomial long division?

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The first step is to divide the leading term of the dividend by the leading term of the divisor.

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

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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 significance of the remainder in polynomial division?

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The remainder indicates what is left over after division; if the remainder is zero, the divisor is a factor of the dividend.

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How do you check if a number is a zero of a polynomial?

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To check if a number is a zero of a polynomial, substitute the number into the polynomial and see if the result equals zero.

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What is the formula for synthetic division?

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Synthetic division uses the coefficients of the polynomial and the zero to perform division without writing out the variables.