How do you factor $y^{3} + y^{2} + 2 y + 14$ $y^3+y^2+2y+14$ ?

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How do you factor $y^{3} + y^{2} + 2 y + 14$ $y^3+y^2+2y+14$ ?

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Answer 1 · 2018-03-05T13:56:37

$(y + 2.47595271) (y^{2} - 1.47595271 y + 5.6543891)$ $(y + 2.47595271)(y^2 - 1.47595271 y + 5.6543891)$

Explanation:

$There are no rational roots.$ $"There are no rational roots."$
$There is no easy factorization as such.$ $"There is no easy factorization as such."$
$The cubic equation has 1 real root that can be factored out.$ $"The cubic equation has 1 real root that can be factored out."$
$That root is y = - 2.47595271 .$ $"That root is "y = -2.47595271.$
$So the factorization is :$ $"So the factorization is : "$
$(y + 2.47595271) (y^{2} - 1.47595271 y + 5.6543891)$ $(y + 2.47595271)(y^2 - 1.47595271 y + 5.6543891)$
$This can be found by a general method to solve cubic equa-$ $"This can be found by a general method to solve cubic equa-"$
$tions like Cardano's method or the substitution of Vieta.$ $"tions like Cardano's method or the substitution of Vieta."$

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How do you factor $y^{3} + y^{2} + 2 y + 14$ $y^3+y^2+2y+14$ ?

1 Answer

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