SOLUTION: What is the value of x? The equation: x^4+7x^3-8x-56=0 There are two values of x and I have only found one, which is -7. I have tried to solve (x^3-8) bit I end up getting a long

Question 856389: What is the value of x? The equation: x^4+7x^3-8x-56=0
There are two values of x and I have only found one, which is -7. I have tried to solve (x^3-8) bit I end up getting a long answer, which is not correct since everyone I know has 2. Thank you for helping me!
Found 3 solutions by edjones, richwmiller, josgarithmetic:
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
x^4+7x^3-8x-56
=x^3(x+7)-8(x+7)
=(x^3-8)(x+7)=0
.
x^3=8
x=2
.
x=-7
.
Ed
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
x^4+7x^3-8x-56=0
There should be four answers since x is to the 4th power.
There are two real and two complex
(x+7) (x^3-8) = 0
(x+7)(x-2)(x^2+2x+4) = 0
x=2
x=-7
x = -1-i sqrt(3)
x = -1+i sqrt(3)
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
How did you find one of the values to be x=-7? If you found this, then perform synthetic division on the given polynomial to continue looking for more roots. (Polynomial division, in case you do not yet know synthetic division).

You keep looking for roots (trying rational roots) until you have found all that you can. Your first successful synthetic division( giving remainder of zero) will give a quotient which will have its own roots, which are also roots of the original polynomial.

-----solution method----

Synthetic Division to check x=-7:
quotient.
-
Synthetic Division on to check for x=2:
quotient.
-
Factorization gives .
-
Using general solution to quadratic equation for roots of the quadratic factor give .... and

The equation has FOUR different solutions for x.
, , ,
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