Polynomial Test Review

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is P(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

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What is the Remainder Theorem?

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The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of this division is equal to f(c).

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How do you find the zeros of a polynomial function?

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To find the zeros of a polynomial function P(x), set P(x) = 0 and solve for x. This can involve factoring, using the quadratic formula, or synthetic division.

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What does it mean for (x - c) to be a factor of a polynomial?

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If (x - c) is a factor of a polynomial P(x), then P(c) = 0. This means that c is a zero of the polynomial.

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What is synthetic division?

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

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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 in a polynomial. It determines the end behavior of the polynomial function.

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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 expression. It indicates the maximum number of zeros the polynomial can have.

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What is the relationship between the degree of a polynomial and the number of zeros?

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A polynomial of degree n can have at most n real zeros, counting multiplicities.

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What is a remainder in polynomial division?

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The remainder is what is left over after dividing a polynomial by another polynomial. It can be found using the Remainder Theorem.

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How do you apply the Remainder Theorem?

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To apply the Remainder Theorem, substitute the value of c into the polynomial f(x) to find the remainder when f(x) is divided by (x - c).