Question

Factor the expression completely. (a2 + 1)2 − 43(a2 + 1) + 442

Answer 1

a^4+2a^2+1-43a^2-43+442
=a^4-41a^2+400
Let x=a^2
x^2-41x+400
make it equal 0 and solve it
41+-sqrt(1681-1600)/2
x1=25
x2=16
So a^2=25
a=+-5
or
a^2=16
a=+-4
So roots of a^4-41a+400 are -5,-4,4,5 so it factors to
(a+5)(a+4)(a-4)(a-5)