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How do you factor #w^2 + 4t^2#?

Answer 1

Nathan Axel

#w^2+4t^2# is already completely factored - at least if you are restricted to real coefficients.

It could factor entirely as follows if complex coefficients were permitted:

#w^2+4t^2 = (w+2it)(w-2it)# (where #i = sqrt(-1)#)

However, the coefficients of neither of these linear factors are entirely real.

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Answer 2

Eli Assouline

The expression (w^2 + 4t^2) cannot be factored further using real numbers because it is a sum of squares. However, it can be factored using complex numbers into the form ((w + 2it)(w - 2it)), where (i) is the imaginary unit, equal to the square root of -1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.