+128475 I'm not sure what you're taught.....but....I see that 2 is a root....so....we can use synthetic division to find the other roots
2 [ 1 -1 0 -2 -4 ]
2 2 4 4
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1 1 2 2 0
Our remaining polynomial is
x^3 + x^2 + 2x + 2
And -1 is a root...so...performing synthetic division again, we have
-1 [ 1 1 2 2 ]
-1 0 -2
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1 0 2 0
The remaining polynomial is
x^2 + 2..... setting this to 0 to find the other roots, we have
x^2 + 2 = 0
x^2 = -2 take both roots
x = ± √2 i
So.....the factorization is :
f(x) = (x - 2) (x + 1) (x - √2 i ) ( x + √2 i )
