How do you factor #v^4+71v^2+70#?

1 Answer
George C.
May 17, 2015

Notice that #71 = 70 + 1# and #70 = 70xx1#.

So we can factor #v^4+71v^2+70 = (v^2+70)(v^2 + 1)#

This is an instance of the identity:
#(x+a)(x+b) = x^2 + (a+b)x + (axxb)#

With #x = v^2#, #a = 70# and #b = 1#.

There are no linear factors with real coefficients because

#v^2 + 70 >= 70 > 0# and #v^2 + 1 >= 1 > 0# for all real values of #v#.

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