Math101 · Independent Ontario learning library
Math101Subtracting Polynomials
Subtracting a polynomial means adding its additive inverse. The negative sign before a bracket changes every term inside; after distribution, like terms combine by adding signed coefficients.
Polynomial subtraction compares models and is needed in division, finite differences, function operations, and algebraic simplification.
Intuition and core definition
Subtracting a polynomial means adding its additive inverse. The negative sign before a bracket changes every term inside; after distribution, like terms combine by adding signed coefficients. Polynomial subtraction is not commutative, so order matters.
Notation, language, and conditions
$P(x)-Q(x)=P(x)+[-Q(x)]$. In vertical layout, align equal powers and subtract each coefficient. Missing powers have coefficient zero. Parentheses are essential around the entire subtracted polynomial.
Why this idea matters
Subtracting a polynomial changes the sign of every term in the subtracted group before like terms may be combined.
A dependable method
- Write both polynomials in standard form with missing-power placeholders if useful.
- Distribute the subtraction sign to every term of the second polynomial.
- Remove parentheses and group like powers.
- Add the signed coefficients.
- Check by adding the result to the subtracted polynomial and recovering the first.
