Write the polynomial as a
product of linear factors,
x^4-5x^2-36

9514 1404 393

  (x +3)(x -3)(x +2i)(x -2i)

Step-by-step explanation:

The factoring to quadratics makes use of the fact that -36 = (-9)(4).

  x^4 -5x^2 -36

  = x^4 -9x^2 +4x^2 -36

  = x^2(x^2 -9) +4(x^2 -9)

  = (x^2 +4)(x^2 -9)

The form for factoring the difference of squares comes into play here. Of course -4 = (2i)^2.

  = (x^2 -(2i)^2)(x^2 -3^2)

  = (x -2i)(x +2i)(x -3)(x +3) . . . factored to linear terms

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