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Find-the-recurring-factors-of-the-polynomial-1-f-x-x-5-6x-4-16x-3-24x-2-20x-8-2-f-x-x-4-x-3-30x-2-7x-56-




Question Number 178957 by Shrinava last updated on 23/Oct/22
Find the recurring factors of the  polynomial:  1. f(x)=x^5 −6x^4 +16x^3 −24x^2 +20x−8  2. f(x)=x^4 −x^3 −30x^2 −7x−56
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{recurring}\:\mathrm{factors}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{polynomial}: \\ $$$$\mathrm{1}.\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{5}} −\mathrm{6x}^{\mathrm{4}} +\mathrm{16x}^{\mathrm{3}} −\mathrm{24x}^{\mathrm{2}} +\mathrm{20x}−\mathrm{8} \\ $$$$\mathrm{2}.\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{3}} −\mathrm{30x}^{\mathrm{2}} −\mathrm{7x}−\mathrm{56} \\ $$
Answered by Frix last updated on 23/Oct/22
1. f(x)=(x−2)(x^2 −2x+2)^2   2. no useable factors
$$\mathrm{1}.\:{f}\left({x}\right)=\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$\mathrm{2}.\:\mathrm{no}\:\mathrm{useable}\:\mathrm{factors} \\ $$

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