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:

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

3 0

3 years ago

For each graph find (a) AB to the nearest tenth and (b) the coordinates of the midpoint of line AB

Lorico [155]

In each graph, they give you a line.

For part A, they want you to use the Distance Formula which is:

$\sqrt{(x2 - x1)^{2}+(y2 - y1)^{2}}$

(x2 is supposed to be x sub 2, but I can't put subheadings in the equation tool)

x1, x2, y1, and y2 are the coordinates of the endpoints of the segment.

For part B, they want you to use the Midpoint Formula, which is:

$(\frac{x1 + x2}{2}, \frac{y1 + y2}{2})$

The coordinate pair you get from the Midpoint Formula is your midpoint.

Hope this helps! :)

3 0

3 years ago