Answer

Given (x+1)^4+(x+3)^4-272

Let

y = x+2
(1)

then

(x+1)^4+(x+3)^4-272

=(y-1)^4+(y+1)^4-272

=(y^2-2y+1)^2+(y^2+2y+1)^2-272

=(y^2+1)^2-4y(y^2+1)+4y^2+(y^2+1)^2+4y(y^2+1)+4y^2-272

=2(y^2+1)^2+8y^2-272

=2y^4+12y^2-270

=2(y^4+6y^2-135)

=2(y^2-9)(y^2+15)

=2(y-3)(y+3)(y^2+15)

Substitute (1) then

(x+1)^4+(x+3)^4-272 = 2(x+5)(x-1)(x^2+4x+19)


Steven Zheng posted 5 hours ago

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