Solving Polynomial Equations

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What is synthetic division and when is it used?

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Synthetic division is a simplified form of polynomial long division. It is used to divide a polynomial by a linear factor of the form (x - c).

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How do you factor a polynomial by grouping?

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To factor by grouping, you group terms in pairs, factor out the common factors from each pair, and then factor out the common binomial factor.

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What are the steps to find the zeros of a polynomial function?

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1. Set the polynomial equal to zero. 2. Factor the polynomial if possible. 3. Use the zero-product property to solve for the variable.

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What is the zero-product property?

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The zero-product property states that if the product of two or more factors is zero, at least one of the factors must be zero.

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What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials or numbers.

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What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms, from the highest degree to the lowest.

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How do you solve a quadratic equation by factoring?

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To solve a quadratic equation by factoring, express the equation in the form ax^2 + bx + c = 0, factor it into (px + q)(rx + s) = 0, and then use the zero-product property.

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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. It determines the end behavior of the polynomial function.

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What is a polynomial equation?

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A polynomial equation is an equation that equates a polynomial expression to zero, typically in the form P(x) = 0.

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What are the different methods to solve polynomial equations?

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Methods include factoring, synthetic division, the quadratic formula, and graphing.