Subtracting Polynomials Generator
The Subtracting Polynomials lesson covers the sign-distribution step in full; this generator drills the result directly, asking you to evaluate the difference of two polynomials at a chosen value — and, at Hard, sometimes in reverse order.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | Subtract two binomials, evaluated at \(x\) | \(P(x)=6x+2\), \(Q(x)=3x-3\), find \((P-Q)(5)\) |
| Medium | Subtract two trinomials, evaluated at \(x\) | Two degree-2 polynomials subtracted |
| Hard | Subtract two trinomials, sometimes in reverse order | \((Q-P)(x)\) as well as \((P-Q)(x)\) |
Easy subtracts two simple binomials, keeping the arithmetic light while the sign-distribution step is still new.
Medium uses two full trinomials, so every term’s sign has to be tracked correctly across three matching-degree pairs.
Hard occasionally reverses which polynomial is subtracted from which, testing directly that \((P-Q)\) and \((Q-P)\) are opposites, not equal.
Using the generator
Pick a difficulty and a question count, and a fresh set appears instantly. Every answer here is a whole number, positive or negative — enter it exactly as computed.
- Check Answers scores the set and flags exactly which problems need another look
- Show Answers reveals every solution, useful for reviewing a paper attempt
- Print Worksheet outputs a clean page for offline practice or classroom handouts
The rules this generator drills
| Rule | Statement |
|---|---|
| Subtraction as adding the opposite | \(A-B = A+(-B)\) |
| Function subtraction | \((P-Q)(x) = P(x) - Q(x)\) |
| Order matters | \((P-Q)\) and \((Q-P)\) are always opposites, never equal |
See the Subtracting Polynomials lesson for the full horizontal and vertical technique, plus why every sign has to flip.
Common mistakes to watch for
Flipping the sign of only the first term. Every term inside the second polynomial’s parentheses changes sign, not just the one next to the minus sign.
Forgetting the negative sign is multiplication by −1. It distributes across the entire polynomial being subtracted, the same way any other multiplication would.
Assuming subtraction is commutative. \((P-Q)(x)\) and \((Q-P)(x)\) are opposites of each other — always subtract in the exact order the problem states.
Combining terms before finishing the sign flip. Distribute the negative sign completely first; combining prematurely risks locking in an unflipped sign.
Where to go next
Once distributing the negative sign feels automatic, the Multiplying Polynomials Generator is the natural next step, since expanding a product depends on tracking signs just as carefully. For the full technique behind every problem here, see the Subtracting Polynomials lesson.