# Solve the polynomials: (1 + x + x^4)(5 + x + x^2 + 3x^2)

Solve the polynomials: $$(1 + x + x^4)(5 + x + x^2 + 3x^2)$$

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Nathalie Redfern

$$(1 + x + x^4)(5 + x + x^2 + 3x^2)$$

$$= 1(5 + x + x^2 + 3x^2) + x(5 + x + x^2 + 3x^2) + x^4(5 + x + x^2 + 3x^2)$$

$$= 5 + x + x^2 + 3x^3 + 5x + x^2 + x^3 + 3x^4 + 5x^4 + x ^5 + x^6 + 3x^7$$

$$= 5 + 6x + 2x^2 + 4x^3 + 8x^4 + x^5 + x^6 + 3x^7$$