Adding Polynomials Practice Problems
Combining like terms — both horizontally and vertically — is covered in full in the Adding Polynomials lesson. Here, that skill gets tested directly: evaluate the sum of two (or three) polynomials at a chosen value and check whether the total comes out right.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | Add two binomials, evaluated at | |
| Medium | Add two trinomials, evaluated at | Two degree-2 polynomials summed |
| Hard | Add three polynomials at once |
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.
Worked examples
One example at each difficulty level, solved the way the practice set expects.
Easy.
Combine like terms:
Medium.
Hard.
The
Using the practice problems
Choose a difficulty and how many questions you want, and a new set appears immediately. Every answer here is a whole number — enter it exactly as computed.
- Check Answers grades the whole set at once and marks exactly which ones to revisit
- Show Answers displays the full solution for every problem, handy for checking work done on paper
- Print Worksheet formats a clean printable page, ideal for offline practice or a classroom handout
The rules these practice problems drill
| Rule | Statement |
|---|---|
| Combining like terms | Add the coefficients; the variable part stays the same |
| Function addition | |
| A missing term | Counts as a coefficient of |
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.
Where to go next
Once adding feels automatic, the Subtracting Polynomials Practice Problems drills the identical skill with one extra sign-distribution step, and the Multiplying Polynomials Practice Problems moves on to FOIL and the box method. For the full technique behind every problem here, see the Adding Polynomials lesson.