Adding and Subtracting Polynomials Calculator
Add or subtract polynomials by combining like terms with step-by-step solutions
Polynomial Calculator
Polynomial P(x)
P(x) = 0
Polynomial Q(x)
Q(x) = 0
Result
Example Calculation
Addition Example
P(x) = 4x⁴ - x³ + 5x + 1
Q(x) = x⁵ + 4x⁴ - 7x³ - 3x² + x + 12
P(x) + Q(x) =
x⁵ + (4 + 4)x⁴ + (-1 + (-7))x³ + (-3)x² + (5 + 1)x + (1 + 12)
= x⁵ + 8x⁴ - 8x³ - 3x² + 6x + 13
Subtraction Example
P(x) - Q(x) =
-x⁵ + (4 - 4)x⁴ + (-1 - (-7))x³ + (0 - (-3))x² + (5 - 1)x + (1 - 12)
= -x⁵ + 0x⁴ + 6x³ + 3x² + 4x - 11
= -x⁵ + 6x³ + 3x² + 4x - 11
Polynomial Terms
Monomial
Single term
Example: 3x²
Binomial
Two terms
Example: x + 2
Trinomial
Three terms
Example: x² + 2x + 1
Key Rules
Only combine like terms (same variable and power)
Add/subtract coefficients of like terms
Keep terms with different powers separate
Write result in descending order of powers
Understanding Polynomial Addition and Subtraction
What are Polynomials?
A polynomial is an algebraic expression consisting of variables and coefficients, involving only non-negative integer powers of the variables. Examples include x² + 2x + 1, 3x³ - 5x + 7.
How to Add Polynomials?
- •Identify like terms (same variable with same exponent)
- •Add the coefficients of like terms
- •Keep unlike terms as separate terms
- •Arrange terms in descending order of powers
How to Subtract Polynomials?
Subtracting polynomials follows the same principle as addition, but you subtract the coefficients of like terms instead of adding them.
General Form:
P(x) ± Q(x) = Σ(a_i ± b_i)x^i
Where a_i and b_i are coefficients of x^i in P(x) and Q(x) respectively.
Remember: When subtracting, distribute the negative sign to all terms in the second polynomial: (a + b) - (c + d) = a + b - c - d