Factor completely n^4 +8n^2 + 15 =

Question

Factor completely
n^4 +8n^2 + 15 =

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Ruby 1 month 2021-09-12T08:18:33+00:00 1 Answer 0

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    2021-09-12T08:19:38+00:00

    Answer:

    The factor form is n^4+8n^2+15 = \quad \left(n^2+3\right)\left(n^2+5\right)

    Step-by-step explanation:

    When it is required to factor the expression given in the problem, we have to first find a common term or terms, which will be found by either grouping the like terms or the splitting of the terms.

    Now the expression that is given here is:

    n^4 +8n^2 + 15

    Now, here we will take:

    u=n^2

    Thus we will get:

    n^4 +8n^2 + 15\\=u^2+8u+15

    Now we will do the middle term split as follows:

    u^2+8u+15\\=\left(u^2+3u\right)+\left(5u+15\right)\\=u\left(u+3\right)+5\left(u+3\right)\\=\left(u+3\right)\left(u+5\right)

    Substituting back u=n^2 , we will have:

    \left(u+3\right)\left(u+5\right)\\=\left(n^2+3\right)\left(n^2+5\right)

    Hence, the required factor form of the given expression will be:

    n^4+8n^2+15 = \quad \left(n^2+3\right)\left(n^2+5\right)

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