STEM PRACTICE AND EVIDENCE WORKBENCH
Expand two entered linear factors and locate leading, middle, or constant coefficient conflicts against a target quadratic.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
Expanding px plus q times rx plus s gives pr x squared plus ps plus qr times x plus qs. The tool compares pr with A, ps plus qr with B, and qs with C separately. Full support requires all three equalities, making a sign or omitted cross product visible instead of returning only a single incorrect label. Supported means the entered factors multiply exactly to the target quadratic. A middle-only conflict often indicates missing or miscombined cross products, while a constant conflict points to q times s. Review greatest common factors, sign arrangements, factor order, chosen number system, zero-product use, and whether the original polynomial is in standard form.
Confirm the question, source, units, notation, response coding, model assumptions, and review threshold. Keep an unchanged copy of the original evidence.
Run the worked example, inspect every intermediate row, and compare it with a hand calculation, diagram, representation, or approved subject method.
Record the method, assumptions, units, classifications, and flagged rows. Verify the editable report independently before educational or laboratory use.
How to interpret the result
Use when a learner has proposed two linear factors and the teacher needs visible evidence about which coefficient fails after expansion. The diagnostic checks integer coefficients and exact algebraic equivalence. It does not find factors, decide irreducibility, extract a greatest common factor, solve roots, accept higher-degree expressions, or assess the reasoning used to propose them.
The difference-of-squares factors expand to x squared minus nine. The monic and nonmonic examples reproduce all target coefficients, including the two cross products for the middle term. The final factors x plus one and x plus four expand to x squared plus five x plus four rather than the target x squared plus six x plus eight, so they are flagged.
Expanding px plus q times rx plus s gives pr x squared plus ps plus qr times x plus qs. The tool compares pr with A, ps plus qr with B, and qs with C separately. Full support requires all three equalities, making a sign or omitted cross product visible instead of returning only a single incorrect label.
Supported means the entered factors multiply exactly to the target quadratic. A middle-only conflict often indicates missing or miscombined cross products, while a constant conflict points to q times s. Review greatest common factors, sign arrangements, factor order, chosen number system, zero-product use, and whether the original polynomial is in standard form.
Do not multiply only first and last terms, add q and s for the constant, omit one cross product, assume two numbers that multiply to C always solve a nonmonic quadratic, lose a negative sign, or stop without expanding. Distribute every term, combine the middle coefficients, and compare all three target coefficients.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, or replace teacher, laboratory, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the approved school system.
No. It describes entered evidence under one disclosed rule. Review reasoning, uncertainty, access, and several evidence sources.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow course and academic-integrity rules.
YOUR NIRMION
