How do I factor 5(x+1)^4 - 5?

[Strat]

How do I factor 5(x+1)⁴ - 5?

I need to solve for x where this equation = 0, but I don't know what to do with (x+1)⁴

If I write it as (x+1)(x+1)(x+1)(x+1), then the zero would at x = -1 but that wouldn't be right.

 

[ksdhart2]

Okay, so you took the first few trivial steps, adding 5 to both sides:

\(\displaystyle 5(x+1)^4-5=0 \implies 5(x+1)^4=5\)

Then dividing both sides by 5:

\(\displaystyle 5(x+1)^4=5 \implies (x+1)^4=1\)

Now, where do you think you'd go from here? Because you have a quartic (4th-degree) polynomial, you know there will be four solutions, but some of them might be complex. Are you concerned with finding all the solutions, or will just the real solutions do?

 

[Deleted member 4993]

How do I factor 5(x+1)⁴ - 5?

I need to solve for x where this equation = 0, but I don't know what to do with (x+1)⁴

If I write it as (x+1)(x+1)(x+1)(x+1), then the zero would at x = -1 but that wouldn't be right.

Can you factorize a² - b² ?

Can you factorize m⁴ - n⁴ ?