Question

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

Answer 1

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:

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