Polynomial Addition

Calculator and example for adding two polynomials

Polynomial Addition Calculator

What is calculated?

This function computes the addition of two polynomials. Coefficients of like powers are added.

Enter polynomials
Input format

Coefficients can be entered as a sequence of numbers separated by semicolons or spaces.

Example: For \(3x^2+4x+5\) enter "3 4 5" or "3; 4; 5"


+
Result
P(x) =
Q(x) =
Sum =
Coefficients of like powers are added

Polynomial Addition Info

Addition rule

Combine like terms:

  • Terms with the same power are combined
  • Coefficients are added
  • Variable and exponent remain
  • Commutative property applies

Tip: Only coefficients of like powers are added.

Quick examples
x² + 2x² = 3x²
Same power
3x + 5x = 8x
Linear terms
2 + 7 = 9
Constant terms
x³ + x = x³ + x
Different powers

Formulas for polynomial addition

General form
\[P(x) + Q(x) = R(x)\] Addition of two polynomials
Add coefficients
\[\sum a_i x^i + \sum b_i x^i = \sum (a_i + b_i) x^i\] Like terms
Degree of result
\[\deg(P + Q) \leq \max(\deg P, \deg Q)\] At most as high as the higher degree
Commutativity
\[P(x) + Q(x) = Q(x) + P(x)\] Order does not matter

Step-by-step example

Example: (3x² + 4x + 5) + (2x + 3)

1Define polynomials

\[P(x) = 3x^2 + 4x + 5\] \[Q(x) = 2x + 3\]

Given polynomials

2Write out terms

P(x) + Q(x) = (3x² + 4x + 5) + (2x + 3)

Write the addition

3Collect like terms

\[= 3x^2 + (4x + 2x) + (5 + 3)\]

Group by powers

4Add coefficients

\[= 3x^2 + 6x + 8\]

Final result

Polynomial Functions

Add  •  Scalar Divide  •  Divide Pointwise  •  Divide with Remainder  •  Multiply  •  Pointwise Multiply  •  Scalar Multiply  •  Subtract  •