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Factor the expression: 2n³ + 22n² + 60n

User Smills
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1 Answer

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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

User Thalm
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