Integrated Math 2 / Unit 2: Polynomials and Factoring
2.1 Adding and Subtracting Polynomials
Notes
A polynomial is a sum of terms with whole-number exponents. Its degree is the highest exponent, and the leading coefficient goes with that term.
- Name by degree: 1 linear, 2 quadratic, 3 cubic. Name by terms: 1 monomial, 2 binomial, 3 trinomial.
- To add, combine like terms: $(3x^2 + 2x - 5) + (x^2 - 4x + 1) = 4x^2 - 2x - 4$.
- To subtract, distribute the negative to every term of the second polynomial first.
- Example: $(5x^2 - 3x + 2) - (2x^2 + x - 6) = 5x^2 - 3x + 2 - 2x^2 - x + 6 = 3x^2 - 4x + 8$.
Practice
Add: $(3x^2 + 2x - 5) + (x^2 - 4x + 1)$.
Combine like terms: $3x^2 + x^2 = 4x^2$, $2x - 4x = -2x$, $-5 + 1 = -4$.
Subtract: $(5x^2 - 3x + 2) - (2x^2 + x - 6)$.
Distribute the negative: the last term becomes $+6$, and $2 + 6 = 8$. Also $-3x - x = -4x$.
What is the best name for $4x^3 - 2x + 7$?
The highest exponent is 3 (cubic) and there are three terms (trinomial).
Ready for more? Take the Unit 2 test.