Polynomials Test Review

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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. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

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How do you classify polynomials by degree?

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Polynomials are classified by their degree: 0 (constant), 1 (linear), 2 (quadratic), 3 (cubic), and so on. The degree is the highest power of the variable in the polynomial.

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What is a trinomial?

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A trinomial is a polynomial that consists of three terms. For example, x^2 + 2x + 1 is a trinomial.

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What is standard form of a polynomial?

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The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 9x^3 + 8x^2 - 3x - 11 is in standard form.

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How do you add polynomials?

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To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = (2 + 4)x^2 + 3x + 5 = 6x^2 + 3x + 5.

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What is a binomial?

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A binomial is a polynomial that consists of two terms. For example, 3x + 5 is a binomial.

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What is the degree of the polynomial 4x^3 - 2x + 7?

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The degree of the polynomial 4x^3 - 2x + 7 is 3, as the highest power of x is 3.

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What is the result of adding (3x^2 + 2) + (5x^2 - 3)?

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The result is (3x^2 + 5x^2) + (2 - 3) = 8x^2 - 1.

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How do you simplify the expression 3x(x + 7)?

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To simplify, distribute 3x: 3x(x + 7) = 3x^2 + 21x.

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What is a cubic polynomial?

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A cubic polynomial is a polynomial of degree 3. It can be expressed in the form ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.