Factoring Polynomials

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What is factoring in polynomials?

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Factoring in polynomials is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.

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What is a polynomial?

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

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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.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.

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What is the Factor Theorem?

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The Factor Theorem states that if a polynomial f(x) has a zero at x = a, then (x - a) is a factor of f(x).

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c).

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How do you find the remainder when dividing polynomials?

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You can find the remainder by using the Remainder Theorem, which states that the remainder of the division of f(x) by (x - c) is f(c).

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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 f(x) by (x - c) is equal to f(c).

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What is the relationship between factors and zeros?

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If (x - a) is a factor of a polynomial, then a is a zero of that polynomial.

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What is the process of polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial of equal or lower degree, similar to long division with numbers.