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Find all real roots of x(x + 1)(x + 2)(x + 3) = 120.

 Jun 16, 2020
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Hi there! so lets break down this question, first we need to expand this into an equation we can solve!

When we expand 

x(x+1)(x+2)(x+3)=120

we get 

\(x^4+6x^3+11x^2+6x=120\)

Now that we have this equation we can start to break down into something we can simplify/factor

\(x^4+6x^3+11x^2+6x−120=120−120 ,\\ x^4+6x^3+11x^2+6x−120=0\)

fun! now we have something we can factor,

\(x^4+6x^3+11x^2-120=0,\\ (x−2)(x+5)(x^2+3x+12)=0 \)

Now we can just look for what value of x makes this new equation equal to zero. 

so we have to make it so that x equals a number that will turn the value into 0 or just set factors into 0. 

I hope that this helps because I dont want to just hand you your answer! If you are still stuck just come back to this thread!

Hope you understand

~ Wolf :D

 Jun 16, 2020

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