Pre Calc 12

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

  • Pre Calc 12 -

    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.

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