A2 - 3.3 Long Division & Synthetic Division

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What is long division in polynomial division?

Back

Long division is a method used to divide polynomials similar to numerical long division, where the dividend is divided by the divisor step by step.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing than 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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How do you find the remainder when dividing a polynomial by a linear factor?

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You can find the remainder by evaluating the polynomial at the value that makes the linear factor zero (using the Remainder Theorem).

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What is the Remainder Theorem?

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The Remainder Theorem states that the remainder of the division of a polynomial p(x) by (x - c) is equal to p(c).

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What does it mean to write an answer in factored form?

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Writing an answer in factored form means expressing a polynomial as a product of its factors, which can help in identifying roots and simplifying expressions.

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What is a coefficient in a polynomial?

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A coefficient is a numerical factor in a term of a polynomial, representing how many times the variable is multiplied.

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What is the significance of placing a zero as a coefficient in a polynomial?

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Placing a zero as a coefficient for a missing exponent ensures that the polynomial maintains its proper degree and structure.

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How do you perform long division with polynomials?

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To perform long division with polynomials, divide the leading term of the dividend by the leading term of the divisor, multiply the entire divisor by this result, subtract, and repeat with the new polynomial.

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What is the leading term of a polynomial?

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The leading term of a polynomial is the term with the highest degree, which determines the polynomial's end behavior.