Polynomial Function 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 f(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 are the zeros of a polynomial?

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The zeros of a polynomial are the values of x for which the polynomial equals zero. They are also known as the roots of the polynomial.

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How do you find the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3)?

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Set the polynomial equal to zero: 3(x + 4)(x + 1)(x - 3) = 0. The zeros are x = -4, x = -1, and x = 3.

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What is factored form of a polynomial?

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Factored form expresses a polynomial as a product of its factors. For example, f(x) = (x - r1)(x - r2)...(x - rn) where r1, r2, ..., rn are the roots of the polynomial.

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What does it mean to factor by grouping?

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Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors. This method is useful for polynomials with four or more terms.

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What is the perimeter of a triangle with sides represented by polynomials?

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The perimeter is the sum of the lengths of all sides. If the sides are represented by polynomials, add the polynomial expressions together.

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How do you multiply two polynomials?

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To multiply two polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

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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. For example, in f(x) = 4x^3 + 2x^2 + 5, the degree is 3.

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What is a leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in f(x) = 3x^4 + 2x^3, the leading coefficient is 3.

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What is the difference between a monomial, binomial, and trinomial?

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A monomial has one term (e.g., 3x), a binomial has two terms (e.g., 3x + 2), and a trinomial has three terms (e.g., 3x^2 + 2x + 1).