Math

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

Calculated Output

x⁴ 1

x³ 1

x² 2

x 5

constant 3

Formula: Distribute every term, then collect like powers

Step-by-Step Breakdown

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

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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.