Polynomial Multiplication Calculator
Free polynomial multiplication calculator. Multiply binomials (ax + b)(cx + d) instantly using FOIL expansion with roots and quadratic term analysis.
Interactive Calculator
1. Provide Details
2. Output Results
Expanded Polynomial (Standard Form)8x² + 2x - 15
Quadratic Term (x²)8x²
Linear Term (x)2x
Constant Term-15
Polynomial Zeros / Rootsx₁ = -1.5000, x₂ = 1.2500
How to Calculate: Formula & Steps
Applies the FOIL (First, Outside, Inside, Last) multiplication algorithm to expand two binomial expressions.
Formula Used:
(ax + b)(cx + d) = (a·c)x² + (a·d + b·c)x + (b·d)Step-by-Step Calculation Example
For (2x + 3)(4x - 5): First = 8x², Outside = -10x, Inside = 12x, Last = -15. Combined: 8x² + 2x - 15.
Common Mistakes to Avoid
- Forgetting to distribute negative signs during multiplication.
- Attempting to add terms with different powers (e.g., x² + x).
Practical Use Cases
- Algebra 1 & Algebra 2 polynomial expansion
- Quadratics factoring and root verification
- Engineering curve model expansions
Expert Tips
- Always write the expanded polynomial in standard descending degree order.
Frequently Asked Questions About Polynomial Multiplication Calculator
How do you multiply two binomials using FOIL?
FOIL stands for First, Outside, Inside, Last. Multiply the First terms of each binomial, then the Outside terms, the Inside terms, and the Last terms, then combine like terms.
How do I find the zeros or roots of a polynomial?
Set each factor equal to zero: ax + b = 0 => x = -b/a, and cx + d = 0 => x = -d/c.
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