Math
Polynomial division.
Definition
The process of dividing one polynomial by another, producing a quotient and possibly a remainder. Long division and synthetic division are the two main methods.
How it works · 5 phases
Step by step.
- Arrange both polynomials in descending order of degree
- Divide the leading term of the dividend by the leading term of the divisor
- Multiply the entire divisor by that result and subtract
- Bring down the next term and repeat until the remainder has lower degree than the divisor
- Write the answer as quotient + remainder/divisor
Examples
Real-world.
- 1 (x³ + 2x² - 5x + 1) ÷ (x - 2) using long division
- 2 Using synthetic division to divide by (x - 3)
- 3 Finding factors of a polynomial by dividing out known zeros
Key Fact
Remainder Theorem: when dividing f(x) by (x - c), the remainder equals f(c)