Polynomials

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A polynomial is an algebraic expression in which the powers of all variables are whole numbers (0, 1, 2, 3, ...). For example: x³ + 2x² - 5x + 7 is a polynomial, but √x + 5 and 1/x - 3 are not polynom…

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The degree of a polynomial in one variable is the highest power of the variable in the polynomial. Example: In p(x) = 2x⁷ - 5x + 9, the highest power is 7, so the degree is 7. For constant polynomials…

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For polynomials with multiple variables, the degree is the highest sum of powers of variables in any single term. Example: In 3m³n⁶ + 7m²n³ - mn, the degrees of terms are: 3+6=9, 2+3=5, 1+1=2. The hig…

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A constant polynomial contains only a constant term with no variables. Examples: 6, -7, 1/2, √3. The degree of any non-zero constant polynomial is 0 because we can write it as 6 = 6x⁰. The degree of z…

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Monomial: Polynomial with one term. Example: 5x³. Binomial: Polynomial with two terms. Example: 3x² + 7. Trinomial: Polynomial with three terms. Example: x² - 4x + 3. These classifications are based o…

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Degree 0: Constant polynomial (Example: 5). Degree 1: Linear polynomial (Example: 2x + 3). Degree 2: Quadratic polynomial (Example: x² + 5x + 6). Degree 3: Cubic polynomial (Example: x³ - 2x + 1). Deg…

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Standard form of a polynomial is when terms are arranged in descending order of powers of the variable. Example: x - 3x² + 5 + x⁴ in standard form becomes x⁴ - 3x² + x + 5. The terms are arranged from…

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Index form includes all missing terms with coefficient zero. Example: x⁴ - 3x² + x + 5 in index form is x⁴ + 0x³ - 3x² + 1x + 5. This form shows every power from the highest degree down to the constan…