Multiplying Polynomials Calculator

Multiply two quadratics to get a degree-4 polynomial.

P₁ x² coeff

P₁ x coeff

P₁ constant

P₂ x² coeff

P₂ x coeff

P₂ constant

x⁴ 1

x³ 1

x² 2

x 5

constant 3

Formula: Distribute every term, then collect like powers

Step-by-step with your numbers:

1. Values used:

2. P₁ x² coeff = 1

3. P₁ x coeff = 2

4. P₁ constant = 1

5. P₂ x² coeff = 1

6. P₂ x coeff = -1

7. P₂ constant = 3

9. x⁴ = 1

10. x³ = 1

11. x² = P₁ x² coeff x P₁ x coeff = 1 x 2 = 2

12. x = 5

13. constant = P₁ x² coeff + P₁ x coeff = 1 + 2 = 3

Did we solve your problem today?

Multiply two quadratic polynomials by distributing every pair of terms and collecting powers.

The math behind it

Each term of the first polynomial multiplies each term of the second. Group results by their power of x to get the final coefficients.

(x² + 2x + 1)(x² − x + 3) = x⁴ + x³ + 2x² + 5x + 3.

What degree is the product?

The sum of the two degrees — here 2 + 2 = 4.