Factor Completely:

10y^7 +26y^6 -12y^5

10y^7 +26y^6 -12y^5

= 2y^5(5y^2 + 13y - 6)
= 2y^5(5y - 2)(y + 3)

To factor completely, we need to find the greatest common factor (GCF) of all the terms in the expression and then factor out the GCF. Let's look at each term separately.

The first term is 10y^7. The prime factors of 10 are 2 and 5. The highest power of y is y^7, so the GCF for this term is 2 * 5 * y^7, which can be written as 10y^7.

The second term is 26y^6. The prime factors of 26 are 2 and 13. The highest power of y is y^6, so the GCF for this term is 2 * 13 * y^6, which can be written as 26y^6.

The third term is -12y^5. The prime factors of 12 are 2, 2, and 3. The highest power of y is y^5, so the GCF for this term is 2 * 2 * 3 * y^5, which can be written as 12y^5.

Now that we have the GCF for all the terms, we can factor it out. The GCF is 2 * 5 * y^5, which can be written as 10y^5.

Factoring out the GCF, we get:
10y^7 + 26y^6 - 12y^5 = 10y^5(y^2 + 2y - 1)

So, the expression can be factored as 10y^5(y^2 + 2y - 1).