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Questions and Answers
Classify the polynomial 2x²+3x-1 by degree and number of terms.
Classify the polynomial 2x²+3x-1 by degree and number of terms.
quadratic trinomial
Classify the polynomial 2x²+3x-13x³-5 by degree and number of terms.
Classify the polynomial 2x²+3x-13x³-5 by degree and number of terms.
cubic polynomial
Classify the polynomial 2x²+3x by degree and number of terms.
Classify the polynomial 2x²+3x by degree and number of terms.
quadratic binomial
Classify the polynomial 2x²+3x-18 by degree and number of terms.
Classify the polynomial 2x²+3x-18 by degree and number of terms.
Classify the polynomial 2x²-12x⁴+1 by degree and number of terms.
Classify the polynomial 2x²-12x⁴+1 by degree and number of terms.
Classify the polynomial 2x²+3x-1-4x⁵ by degree and number of terms.
Classify the polynomial 2x²+3x-1-4x⁵ by degree and number of terms.
Classify the polynomial 2x²+3x by degree and number of terms.
Classify the polynomial 2x²+3x by degree and number of terms.
Classify the polynomial 3x-15x²-3 by degree and number of terms.
Classify the polynomial 3x-15x²-3 by degree and number of terms.
Classify the polynomial 2x²+3x by degree and number of terms.
Classify the polynomial 2x²+3x by degree and number of terms.
Classify the polynomial 2x²+3x-16x³+3 by degree and number of terms.
Classify the polynomial 2x²+3x-16x³+3 by degree and number of terms.
Classify the polynomial 3x-13x⁴-5 by degree and number of terms.
Classify the polynomial 3x-13x⁴-5 by degree and number of terms.
Classify the polynomial 2x²+3x-2 by degree and number of terms.
Classify the polynomial 2x²+3x-2 by degree and number of terms.
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Study Notes
Polynomial Classification Overview
- Polynomials can be classified based on their degree (the highest exponent) and number of terms (monomial, binomial, trinomial).
Degree and Number of Terms
-
Quadratic: A polynomial of degree 2.
- Example: 2x² + 3x - 1 (quadratic trinomial)
- Example: 2x² + 3x (quadratic binomial)
-
Cubic: A polynomial of degree 3.
- Example: 2x² + 3x - 16x³ + 3 (cubic polynomial)
- Example: 2x² + 3x - 13x³ - 5 (cubic polynomial)
-
Quartic: A polynomial of degree 4.
- Example: 2x² - 12x⁴ + 1 (quartic trinomial)
- Example: 3x - 13x⁴ - 5 (quartic trinomial)
-
Quintic: A polynomial of degree 5.
- Example: 2x² + 3x - 1 - 4x⁵ (quintic polynomial)
Examples and Classifications
- 2x² + 3x - 1: Quadratic trinomial with three terms.
- 2x² + 3x - 13x³ - 5: Cubic polynomial, includes degree 3 term.
- 2x² + 3x: Quadratic binomial, contains two terms.
- 3x - 15x² - 3: Quadratic trinomial, consistent with quadratic classification.
- 2x² + 3x - 2: Quadratic trinomial, follows the pattern of degree 2 and three terms.
Summary of Key Classifications
- Monomial: A polynomial with a single term.
- Binomial: A polynomial with two terms (the sum of two monomials).
- Trinomial: A polynomial with three terms (the sum of three monomials).
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