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