Adding and Subtracting Polynomials Calculator

Polynomial addition and subtraction relies on the principle of combining like terms—terms that contain the same variables raised to the exact same powers. For two polynomials, say P(x) and Q(x), you align the coefficients of matching degree exponents. When adding, you compute $A_n + B_n$ for each coefficient index $n$. When subtracting, you find $A_n - B_n$, effectively distributing the negative sign across every term in the second polynomial. Our calculator processes coefficients from $A_0$ through $A_6$ and $B_0$ through $B_6$ to deliver an immediate, fully simplified resultant expression.

Let us walk through adding two quadratic polynomials: P(x) = 3x² + 5x + 2 and Q(x) = 1x² - 2x + 4. Here, our coefficients are A₂ = 3, A₁ = 5, A₀ = 2, and B₂ = 1, B₁ = -2, B₀ = 4. To add them, we group the like terms by their powers of x. First, combine the quadratic terms: 3x² + 1x² = 4x². Next, combine the linear terms: 5x + (-2x) = 3x. Finally, combine the constant terms: 2 + 4 = 6. Assembling these results gives our final simplified polynomial: 4x² + 3x + 6.

Always double-check your input signs, especially when subtracting polynomials, as failing to distribute the negative sign to every term in the second expression is the most common error in algebra. Keep your terms written in standard form—descending order of exponents—before entering them into any calculator to maintain clarity. If a particular degree term is missing from your polynomial, simply input a coefficient of zero to keep your placeholders accurate.