Divide Polynomials and Factor Polynomials

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What is Synthetic Division?

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A method used to divide a polynomial by a linear divisor of the form (x - c) using coefficients.

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What is Long Division in Polynomials?

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A method for dividing polynomials similar to numerical long division, used when the divisor is not a linear polynomial.

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How do you perform Synthetic Division?

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1. Write down the coefficients of the polynomial. 2. Use the root of the divisor (c) to perform the division. 3. Bring down the leading coefficient and multiply it by c, then add to the next coefficient. Repeat until finished.

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What is the Remainder Theorem?

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If a polynomial f(x) is divided by (x - c), the remainder is f(c).

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What is the Factor Theorem?

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A polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

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How do you factor a polynomial?

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To factor a polynomial, find its roots or use methods like grouping, synthetic division, or applying the quadratic formula.

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What is the difference between factoring and dividing polynomials?

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Factoring breaks down a polynomial into simpler components, while dividing polynomials finds how many times one polynomial fits into another.

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What is a polynomial?

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An expression consisting of variables raised to non-negative integer powers and coefficients.

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What is a linear polynomial?

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A polynomial of degree 1, in the form of ax + b, where a and b are constants.

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What is a quadratic polynomial?

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A polynomial of degree 2, in the form of ax² + bx + c, where a, b, and c are constants.