10.1 Classify Polynomials with Add/Sub

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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 whole number powers and coefficients. For example, 2x^2 + 3x - 5 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 polynomial. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

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How do you classify polynomials based on the number of terms?

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Polynomials can be classified as: 1. Monomial (1 term), 2. Binomial (2 terms), 3. Trinomial (3 terms), and 4. Polynomial (more than 3 terms).

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What is the result of subtracting two polynomials?

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When subtracting two polynomials, you subtract the coefficients of like terms. For example, (3x^2 + 2x) - (x^2 + 4x) = 2x^2 - 2x.

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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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How do you find the difference of two polynomials?

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To find the difference, subtract the second polynomial from the first by combining like terms. For example, (2x^2 + 3x) - (x^2 + 2) = x^2 + 3x - 2.

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What is the 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, 4x^3 + 2x^2 - x + 5 is in standard form.

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What does it mean for a polynomial to be in descending order?

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A polynomial is in descending order when the terms are arranged from the highest degree to the lowest degree. For example, 5x^4 - 3x^2 + 2 is in descending order.

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What is a quartic polynomial?

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A quartic polynomial is a polynomial of degree 4. For example, 2x^4 + 3x^3 - x + 1 is a quartic polynomial.