Solve n³ + 2n² - 15n = 0 by factoring. Show the factored form of the equation, and the resulting solutions.

Answer: n = 0

n = 3

n = - 5

Step-by-step explanation:

The given cubic equation is expressed as

n³ + 2n² - 15n = 0

Since n is common to each term, we would factorize n out. It becomes

n (n² + 2n - 15) = 0

n = 0 or

n² + 2n - 15 = 0

To further factorize the quadratic equation, we would would find two numbers such that their sum or difference is 2n and their product is - 15n². The two numbers are 5n and - 3n. Therefore,

n² + 5n - 3n - 15 = 0

n (n + 5) - 3 (n + 5) = 0

(n - 3) (n + 5) = 0

n = 3 or n = - 5

Step-by-step explanation:

Take n common

n (n²+2n-15) = 0

now factorise the quadratic one as n when goes to RHS it becomes zero

n²-3n+5n-15=0

n (n-3) + 5 (n-3) = 0

n=3,-5