Question

Select the correct answer from the drop-down menu.

Find the trinomial.
(a^2- 6) and (a^2+ 4) are the factors of

a^4 + 2a^2 + 24
a^4 - 2a^2 - 24
a^4 + 2a^2 - 24
a^4 - 2a^2 +24

Answer 1

`a^4 -2a^2 -24`

Explanation:

Given

`(a^2- 6) \ and\ (a^2+ 4)`

Required

Find the trinomial

Let T represents the trinomial;

To calculate the trinomial, we simply multiply the above factors;

This done as follows;

`T = (a^2 - 6)(a^2 +4)`

Expand

`T = a^2(a^2 +4) -6(a^2 +4)`

Open bracket

`T = a^2*a^2 +a^2*4 -6*a^2 -6 * 4`

`T = a^4 +4a^2 -6a^2 -24`

`T = a^4 -2a^2 -24`

The above can not be solved any further; hence, the trinomial is
`a^4 -2a^2 -24`