Answer:
The factor form is [tex]n^4+8n^2+15 = \quad \left(n^2+3\right)\left(n^2+5\right)[/tex]
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:
[tex]n^4 +8n^2 + 15[/tex]
Now, here we will take:
[tex]u=n^2[/tex]
Thus we will get:
[tex]n^4 +8n^2 + 15\\=u^2+8u+15[/tex]
Now we will do the middle term split as follows:
[tex]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)[/tex]
Substituting back [tex]u=n^2[/tex] , we will have:
[tex]\left(u+3\right)\left(u+5\right)\\=\left(n^2+3\right)\left(n^2+5\right)[/tex]
Hence, the required factor form of the given expression will be:
[tex]n^4+8n^2+15 = \quad \left(n^2+3\right)\left(n^2+5\right)[/tex]
