For this case we must factor the following expression:
[tex]5y ^ 4 + 11y ^ 2 + 2[/tex]
We rewrite[tex]y^ 4[/tex] as[tex](y^ 2) ^ 2[/tex]:
[tex]5 (y ^ 2) ^ 2 + 11y ^ 2 + 2[/tex]
We make a change of variable:
[tex]u = y ^ 2[/tex]
So, we have:
[tex]5u ^ 2 + 11u + 2[/tex]
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:[tex]5u ^ 2 + (1 + 10) u + 2\\5u ^ 2 + u + 10u + 2[/tex]
We factor the highest common denominator of each group:
[tex]u (5u + 1) +2 (5u + 1)[/tex]
We factor [tex](5u + 1):[/tex]
[tex](5u + 1) (u + 2)[/tex]
Returning the change:
[tex](5y ^ 2 + 1) (y ^ 2 + 2)[/tex]
ANswer:
[tex](5y ^ 2 + 1) (y ^ 2 + 2)[/tex]
