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Math Help - [SOLVED] please respond asap, really important :)

  1. #1
    softballprostar18
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    Question [SOLVED] please respond asap, really important :)

    I would apprieciate any and all feedback regarding the following problem. Thank you soooo much!

    1. The expression x^4 + x^2 +1 cannot be factored using known techniques. However, by writing x^2 as 2x^2 -x^2, we obtain
    x^4 + 2x^2 +1 -x^2 which can be factored using a difference of squares.

    eg. x^4 +2x^2 +1 -x^2 = (x^2+1)^2 - x^2
    = (x^2 + x + 1) (x^2 - x +1)

    Use this technique to factor:

    a) x^4 + 5x^2 + 9

    b) 4x^4 + 8x^2 +9
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  2. #2
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    Let's look at (a). The hint suggest writing it as a difference of two squares by adding and subtracting a suitable square. Aboyut the first thing we think of is to add and subtract x^2:

    x^4 + 5x^2 + 9 + x^2 - x^2 = (x^4 + 6x^2 + 9) - x^2 = (x^2+3)^2 - x^2 = (x^2+3+x)(x^2+3-x)

    For (b) the hint is to add and subtract 4x^2 ...
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