Question 1166349
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<pre>

If  x-2  is the factor of  f(x) = x^4 - 5x^2 + k,

it means that the real number of 2 is the root to this polynomial   (the Remainder theorem).



So we substitute x= 2 into the polynomial and equate it to zero

    f(2) = 2^4 - 5*2^2 + k = 0.


It leads us to

          16 - 5*4 + k = 0

          16 - 20 + k = 0

          -4      + k = 0

          k = 4.      <U>ANSWER</U>
</pre>

Solved.


See how simple is it ?