Answer:
2n(n + 5)(n + 6)
Explanation:
given the expression
2n³ + 22n² + 60n ← factor out the common factor of 2n from each term
= 2n(n² + 11n + 30) ← factorise the quadratic
consider the factors of the constant term (+ 30) which sum to give the coefficient of the n- term (+ 11)
the factors are + 5 and + 6 , since
+ 5 × + 6 = + 30 and 5 + 6 = + 11
use these factors to split the n- term
n² + 5n + 6n + 30 ( factor the first/second and third/fourth terms )
= n(n + 5) + 6(n + 5) ← factor out (n + 5) from each term
= (n + 5)(n + 6)
Then
2n³ + 22n² + 60n
= 2n(n + 5)(n + 6) ← in factored form