SOLUTION: (x+1)(x+2)(x+3)(x+4) = 120

Question 126457: (x+1)(x+2)(x+3)(x+4) = 120
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
An analytical way of doing this problem is to look at the factors of 120.
.
Divide it by 2 and you get 60*2
.
Divide the 60 by 4 to get 4 and 15 as factors of 60 and you have that the factors of 120
have become 4*15*2.
.
Then factor 15 into 5*3 and substitute that result for 15 to get that the factors of 120
are 4*3*5*2. If you multiply these factors together you do get 120, so our factors check out
to be OK.
.
Now arrange the factors in ascending order: 2*3*4*5
.
Notice significantly that each of these factors increases by 1. Now compare them to the
factors on the left side of the problem you were given ...
.
(x+1)*(x+2)*(x+3)*(x+4)
.
Each of those factors is 1 greater than the preceding factor ... and there are four of them
just as we found in the four factors 2*3*4*5
.
What do we get if we set the first factor x + 1 equal to 2 ... we find x = 1
.
What do we get if we set the second factor x + 2 equal to 3 ... we again find x = 1
.
What do we get if we set the third factor x + 3 equal to 4 ... we again find x = 1
.
And, finally, what do we get if we set the fourth factor x + 4 equal to 5 ... we again find x = 1
.
What an interesting outcome. If in each of the four factors:
.
(x+1)*(x+2)*(x+3)*(x+4)
.
we set x = 1, the factors become 2*3*4*5 and this product is 120. So the solution
to this problem is x = 1
.
Sure was a lot easier to do it this way than to try multiplying out the 4 original factors
and then setting that product equal to 120 and trying to solve that fourth order equation.
.
Hope this is clear enough so that you can follow it through and see what was done to solve
the problem.
.

RELATED QUESTIONS
(X+1)(2+x )(3+x... (answered by jsmallt9)

Solve:(X 3)(x... (answered by Fombitz)

for what value of x does 1 + 2 +... (answered by rothauserc)

if f(-3)=-120, for f(x)=x^4+x^3-19x^2+kx+30.. find... (answered by josh_jordan)

Four expressions are shown below 1- 2(2x�-2x-60) 2- 4(x�-x-30) 3- 4(x+6)(x-5) (answered by MathTherapy)

(x-1)(x+1)(x)=120 (answered by Alan3354)

log(120-x)=2 (answered by stanbon,Raktim)

Factorise... (answered by josgarithmetic,Edwin McCravy)

X^4-1/X^3+X^2+X+1 (answered by Edwin McCravy)