A polynomial combines powers of a variable with coefficients. Its structure lets terms be expanded, combined, divided, or factored by precise rules.
Use it to make the expression’s terms and factors visible before interpreting a result.
The relationship
Write the rule before calculating
Find u,v such that uv = product and u+v = sum.
See the structure
What the calculation is doing
x²+ 3x+ 2Find u,v such that uv = product and u+v = sum.
Worked interpretation
Read the result in context
Enter the example values shown in the fields to verify the stated relationship.
Interpret with care
Important boundary
Factoring and cancellation can lose roots or change domains if a zero factor is silently divided away.
Use the Mathematics collection to move between connected concepts without duplicating the calculation.
Quick guide
How to use this calculator
Enter values using the notation shown beside each field.
Choose a calculation mode when the tool offers more than one interpretation.
Read the primary answer first, then inspect the supporting details.
Calculation method
Apply the stated definition
Find u,v such that uv = product and u+v = sum.
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
Enter the example values shown in the fields to verify the stated relationship.
Find u,v such that uv = product and u+v = sum.
Supported inputs
Precision and limits
Finite, bounded input
Numeric inputs use finite JavaScript floating-point values with magnitude limits. Results are normally displayed to 12 significant digits; outputs labelled approximate are not exact identities.
Notation
Enter ordinary finite decimals. Polynomial fields use coefficients in descending powers, separated by commas; for example 1, −3, 2 means x² − 3x + 2.
