Question

Factor the higher degree polynomial


5y^4 + 11y^2 + 2

Answer 1

`5y^4 + 11y^2 + 2=\\5y^4+10y^2+y^2+2=\\5y^2(y^2+2)+1(y^2+2)=\\(5y^2+1)(y^2+2)`

Answer 2

For this case we must factor the following expression:

`5y ^ 4 + 11y ^ 2 + 2`

We rewrite
`y^ 4` as
`(y^ 2) ^ 2`:

`5 (y ^ 2) ^ 2 + 11y ^ 2 + 2`

We make a change of variable:

`u = y ^ 2`

So, we have:

`5u ^ 2 + 11u + 2`

we rewrite the term of the medium as a sum of two terms whose product is 5 * 2 = 10 and whose sum is 11. Then:
`5u ^ 2 + (1 + 10) u + 2\\5u ^ 2 + u + 10u + 2`

We factor the highest common denominator of each group:

`u (5u + 1) +2 (5u + 1)`

We factor
`(5u + 1):`

`(5u + 1) (u + 2)`

Returning the change:

`(5y ^ 2 + 1) (y ^ 2 + 2)`

ANswer:

`(5y ^ 2 + 1) (y ^ 2 + 2)`