Question

Four consecutive integers have a product of 360 Find the integers by writing a plynomial equation that represents the integers and then solving algebraically.

Answer 1

let the numbers be
x-1 x x+1 x+2
then
x(x-1)(x+1)(x+2) = 360

since the numbers are all about equal, and since 256 = 4^4, I'd say the numbers are

3,4,5,6

algebraically,
x^4+2x^3-x^2-2x-360 = 0

you know the roots are all factors of 360, and you'd like to try numbers near 4, some synthetic division will quickly show that the solutions are 3,4,5,6.