Polynomial Operations
Polynomial Analysis
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📚 Polynomial Information
Input Format
Enter polynomials using standard notation:
Examples:
• x^2 + 3x - 4
• 2x^3 - 5x^2 + x + 7
• x^4 - 1
• 3x - 2
• x^2 + 3x - 4
• 2x^3 - 5x^2 + x + 7
• x^4 - 1
• 3x - 2
Note: Use ^ for exponents, * for multiplication (optional), and standard operators +, -, *, /
Polynomial Operations
Addition: Combine like terms
(2x² + 3x) + (x² - x + 5) = 3x² + 2x + 5
Subtraction: Subtract corresponding terms
(2x² + 3x) - (x² - x + 5) = x² + 4x - 5
Multiplication: Distribute and combine
(x + 2)(x - 3) = x² - 3x + 2x - 6 = x² - x - 6
Finding Roots
Methods used based on polynomial degree:
Linear (ax + b): x = -b/a
Quadratic (ax² + bx + c): Quadratic formula
x = (-b ± √(b² - 4ac)) / (2a)
Higher degrees: Numerical methods and factoring
Polynomial Properties
Degree: Highest power of the variable
Leading Coefficient: Coefficient of highest degree term
Constant Term: Term with no variable
Standard Form: Terms ordered by decreasing degree
5x³ - 2x² + 7x - 3
Degree: 3, Leading coefficient: 5, Constant: -3
Degree: 3, Leading coefficient: 5, Constant: -3