Pl tell me the factorization x^3-12x^2+47x+60. first factor is (x+1), why should i go for x+3 when -1 sat?

Question

(x+1) satisfy. why go for (x-3). explain please

Answer 1

There is a formula to compute cubic roots but why bother.

you are correct (if the equation is as written) that (x+1) is a factor.

The other two roots are 6.5 ± (√17.75)i ≈ 6.5 ± 4.21i

obviously ±3 are not root and (x+3) and (x-3) are irrelevant.

Your question why should I go for x+3 implies that you did not state all pertinent information in your question.  

Why should you go for 1000x² - √2 ? Makes no sense as written

Answer 2

divide (x^3-12x^2+47x+60) by (x+1)

the quotient is (x^2 - 13x + 60)

this is not factorable anymore on the rational set.

you do not go for (x-3).. . .

(x^3-12x^2+47x+60) = (x+1) * (x^2 - 13x + 60)