Adding and Subtracting Polynomials
I can add and subtract polynomials by giving the minus sign to every term.
The problem this sheet solves
Subtracting polynomials fails on sign distribution, and it fails quietly: both the right and the wrong answer begin with the same leading term, so checking the front of the expression proves nothing. Only the middle term and the constant tell them apart, and those are the parts students check last, if at all. This sheet changes every sign FIRST and combines second, making the subtraction into an addition problem students already handle. Algebra tiles show why unlike terms cannot merge, and the sheet is explicit that the leading term is a useless check here, which redirects attention to where the error actually lives.
The key rule
A minus in front of a bracket is −1 times EVERY term inside. Change all the signs first, then combine like terms.
Every term, not just the first.
Watch out
The mistake: A student writes 3x2 − x − 1, negating only the 2x2.
The fix: 3x2 + 7x − 3. Both answers begin 3x2, so checking the leading term proves nothing — only the middle term and the constant tell them apart.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.