Polynomials Test

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 1 is a 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 expression. For example, in the polynomial 4x^3 + 2x^2 + x, the degree is 3.

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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 binomial of the form (x - c). It is faster than long division and is used primarily for polynomials.

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How do you determine the number of zeros needed in synthetic division?

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The number of zeros needed in synthetic division corresponds to the degree of the polynomial minus the number of terms in the polynomial. For example, for x^6 + 4x^3 + 2, you need 4 zeros.

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What is the classification of the polynomial x^2 + 4x - 8?

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The polynomial x^2 + 4x - 8 is classified as a quadratic polynomial because its highest degree is 2.

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What is multiplicity in polynomials?

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Multiplicity refers to the number of times a particular root or factor appears in a polynomial. For example, in (x + 5)^2, the factor (x + 5) has a multiplicity of 2.

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What is a binomial?

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A binomial is a polynomial that contains exactly two terms. For example, 3x + 4 is a binomial.

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What is a trinomial?

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A trinomial is a polynomial that contains exactly three terms. For example, x^2 - 5x + 6 is a trinomial.

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What is the coefficient of a term in a polynomial?

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The coefficient is the numerical factor in front of a term in a polynomial. For example, in 3x^2, the coefficient is 3.

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How do you find the sum of two polynomials?

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To find the sum of two polynomials, combine like terms. For example, (x^2 - 4x + 3) + (3x^2 - 3x - 5) results in 4x^2 - 7x - 2.