Algebra I
Adding and Subtracting Polynomials
Lesson
A polynomial is a sum of terms like , , or . Adding or subtracting polynomials is just combining like terms — the same skill as before, but now we have terms with different exponents.
Two terms are like terms only if they have the same variable raised to the same exponent:
- and are like (both ).
- and are NOT like (different exponents).
- Constants are like terms with each other.
To subtract a polynomial, distribute the negative sign across every term inside the parentheses, then combine like terms.
Worked example 1 — adding
Group like terms:
Combine each group:
Worked example 2 — subtracting
Distribute the negative sign across the second polynomial — every sign flips:
Combine like terms:
How to type your answer
Write terms in descending order of exponent (highest first). Use ^ for exponents. No spaces. Use x for . Examples: 4x^2-2x+2, 3x^2-4x+5, x^2+5.
Practice
Work through these. Stuck? Click Get a hint.
Warm-Up
Quick problems to get going.
Problem 1
Problem 2
Problem 3
Problem 4
Practice
Standard problems matching the lesson.
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Challenge
Harder problems — edge cases, trickier numbers, multiple steps.
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22