Question

How do you factor `2a ^ { 4} - a ^ { 2} - 10`?

Answer 1

`( 2a^2 -5 )( a^2 + 2)`

Explanation:

The trinomial is the form `" " Ax^2 + Bx - C`

The C term is negative so one binomial factor must be positive an the other binomial factor must be positive.

The B term is negative so the product of the negative terms must be greater than the the positive terms.

The A term has factors of 2 and 1.

The possible combinations are:

1 x 10 : 2 x 1 difference of eight

     2x 10 :  1 x 1 difference of 19

     2 x 5  : 1 x 2  difference of eight

      2x 2  :  1 x 5  difference of one so this is the combination that works

The five must be negative and the four positive so the factors are:
`( 2a^2 -5) ( a^2 + 2)`

Check by finding the product:
`( 2a^2 -5) ( a^2 + 2)`
`= 2a^4 - 5a^2 + 4 a^2 -10 " "` adding gives
`2a^4 - a^2 - 10`