What is factor x^5+12x^4+36x^3+5x^2+60x+180 ?

The solution to factor x^5+12x^4+36x^3+5x^2+60x+180 is (x+6)^2(x^3+5)

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factor x^5+12x^4+36x^3+5x^2+60x+180

factor

x^{5} + 12 x^{4} + 36 x^{3} + 5 x^{2} + 60 x + 180

(x + 6)^{2} (x^{3} + 5)

Solution steps

x^{5} + 12 x^{4} + 36 x^{3} + 5 x^{2} + 60 x + 180

= (x^{5} + 12 x^{4} + 36 x^{3}) + (5 x^{2} + 60 x + 180)

Factor out

x^{3}

from

x^{5} + 12 x^{4} + 36 x^{3} : x^{3} (x^{2} + 12 x + 36)

Factor out

5

from

5 x^{2} + 60 x + 180 : 5 (x^{2} + 12 x + 36)

= x^{3} (x^{2} + 12 x + 36) + 5 (x^{2} + 12 x + 36)

Factor out common term

x^{2} + 12 x + 36

= (x^{2} + 12 x + 36) (x^{3} + 5)

Factor

x^{2} + 12 x + 36 : (x + 6) (x + 6)

= (x + 6) (x + 6) (x^{3} + 5)

Apply exponent rule:

aa = a^{2}

(x + 6) (x + 6) = (x + 6)^{2}

= (x + 6)^{2} (x^{3} + 5)

lo g_{2} (∣ x ∣) = 5

18 + p > 4

x - 6 = 15

- 3 < x \leq 0

2 x^{2} - 15 x - 2 = 0

What is factor x^5+12x^4+36x^3+5x^2+60x+180 ?
The solution to factor x^5+12x^4+36x^3+5x^2+60x+180 is (x+6)^2(x^3+5)