Adding Polynomials Generator
The Adding Polynomials lesson covers combining like terms in full, both horizontally and vertically; this generator drills the result of that combining directly, asking you to evaluate the sum of two (or three) polynomials at a chosen value.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | Add two binomials, evaluated at \(x\) | \(P(x)=4x-3\), \(Q(x)=2x+7\), find \((P+Q)(-5)\) |
| Medium | Add two trinomials, evaluated at \(x\) | Two degree-2 polynomials summed |
| Hard | Add three polynomials at once | \((P+Q+R)(x)\) |
Easy adds two simple binomials, keeping the arithmetic light while the “evaluate the sum” idea is still new.
Medium uses two full trinomials, so combining like terms correctly matters across three matching-degree pairs instead of one.
Hard adds three polynomials in a single problem, the same skill extended one step further — exactly where a term is most likely to get lost without a careful column-by-column check.
Using the generator
Pick a difficulty and a question count, and a fresh set appears instantly. Every answer here is a whole number — 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 |
|---|---|
| Combining like terms | Add the coefficients; the variable part stays the same |
| Function addition | \((P+Q)(x) = P(x) + Q(x)\) |
| A missing term | Counts as a coefficient of \(0\) in that position |
See the Adding Polynomials lesson for the full horizontal and vertical technique, plus how to handle more than one variable.
Common mistakes to watch for
Combining terms that only look similar. A degree-2 term and a degree-1 term are never like terms, no matter how close their coefficients are.
Losing a term when one polynomial is missing it. A missing term contributes nothing to that position — it doesn’t shift the remaining terms.
Adding exponents instead of coefficients. Combining like terms only ever changes the coefficient; the exponent stays exactly as it was.
Skipping the evaluate-each-piece-separately check. \((P+Q)(x)\) always equals \(P(x)+Q(x)\) — evaluating each polynomial on its own first is a reliable way to double-check a combined answer.
Where to go next
Once adding feels automatic, the Subtracting Polynomials Generator drills the identical skill with one extra sign-distribution step, and the Multiplying Polynomials Generator moves on to FOIL and the box method. For the full technique behind every problem here, see the Adding Polynomials lesson.