Adding and multiplying polynomials
Add, subtract and multiply polynomials, then arrange in descending powers of x.
Key formulas
Like terms
Only terms with the same variables and powers combine. 3x² and −5x² make −2x²; 3x² and 3x do not combine.
Multiplication
Distribute carefully with signs. (2x)(3x − 5) = 6x² − 10x. For two binomials, produce four products then collect.
Descending powers checklist
After simplifying, reorder: cubic, quadratic, linear, constant. Many MCQ items test recognition of this order rather than heavy algebra.
Exam habit
Box the degree of the answer — degree adds when multiplying leading terms (if no cancellation).
Worked example
Add polynomials
Problem. Simplify (3x² − 2x + 5) + (x² + 7x − 1).
Solution. 4x² + 5x + 4.
Review quiz
1 / 4(3x²−2x+5)+(x²+7x−1) =
Practice questions
- Simplify (3x² − 2x + 5) + (x² + 7x − 1).
- Simplify (4x − 3) − (2x + 9).
- Expand 3x(2x − 5).
- Which is in descending powers of x: 2x − x³ + 1 or −x³ + 2x + 1?
Study notes
What is the degree of 5?
A non-zero constant has degree 0.
Is x + 1/x a polynomial?
No — negative powers are not allowed in polynomials.