How should I factor this polynomial: x^3-x^2-4x-6

eszkortwxp

eszkortwxp

Answered question

2022-04-23

How should I factor this polynomial: x3x24x6

Answer & Explanation

Jonas Dickerson

Jonas Dickerson

Beginner2022-04-24Added 22 answers

Typically when you have a polynomial of the form
f(x)=xn+a1xn1+a2xn2++an
where akZ, to factorize it, it is a good idea to first plug in the values of the divisors of an in f(x) with the hope that it will evaluate to 0. In your case, the polynomial is
f(x)=x3x24x6
The divisors of -6 are [±1,±2,±3]. We find that f(±1)0,f(±2)0 and f(3)0, while f(3)=0
Hence we have f(x)=(x3)(x2+ax+b). We get that 3b=6 and a3=1. Hence, we get that b=2 and a=2. Hence
f(x)=(x3)(x2+2x+2)
=(x3)((x+1)2+1)=(x3)(x+1i)(x+1+i)

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