Adding and Subtracting Polynomials
Combine like terms; distribute the negative when subtracting.
About this topic
To add polynomials, combine like terms by adding the coefficients of terms with the same variable and exponent. To subtract, distribute the minus sign to every term of the second polynomial first, then combine.
Writing the polynomials in standard form and lining up like terms in columns helps avoid slips. For (3x² + 2x − 5) + (x² − 4x + 1), the x² terms give 4x², the x terms give −2x, and the constants give −4, so the sum is 4x² − 2x − 4. For subtraction, (3x² + 2x − 5) − (x² − 4x + 1) becomes 3x² + 2x − 5 − x² + 4x − 1 = 2x² + 6x − 6.
The idea matches combining similar objects: you can add 3 apples and 2 apples, but not apples and oranges. In practice this models total profit as revenue polynomial minus cost polynomial, or the combined area of several shapes.
The most common error is forgetting to change the sign of every term in the subtracted polynomial, especially the last one. Another is adding exponents: 3x² + 4x² is 7x², not 7x⁴. Only coefficients change when combining like terms.
Key ideas
- Align like terms
- Change every sign when subtracting
- Result is still a polynomial
Quick check
Use cases: where Adding and Subtracting Polynomials helps
- Homework: review the key idea behind Adding and Subtracting Polynomials before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Adding and Subtracting Polynomials without notes.
- Visual learning: play with the interactive lab to see how Adding and Subtracting Polynomials changes when you adjust its inputs.
- Teaching a friend: explain Adding and Subtracting Polynomials in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Adding and Subtracting Polynomials?
Combine like terms; distribute the negative when subtracting.
What will I learn in Adding and Subtracting Polynomials?
Align like terms. Change every sign when subtracting. Result is still a polynomial.
Is Adding and Subtracting Polynomials part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Adding and Subtracting Polynomials lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Adding and Subtracting Polynomials?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.