Factor the polynomial by its greatest common monomial factor. 20y^6-15y^4+40y^2=20y 6 −15y 4 +40y 2 =20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared, equals

 To factor the polynomial 20y^6 − 15y^4 + 40y^2 by its greatest common monomial factor, we first need to identify the common factor in each term. We look at both the coefficients (numeric parts) and the variables (literal parts) of each term.

Looking at the coefficients (20, -15, 40), we can see that the greatest common factor (GCF) is 5. Now we need to look at the variables. Here, each term contains a power of y, so we find the smallest power of y that is present in every term. The smallest power of y is y^2.

So, the greatest common monomial factor is 5y^2.

Next, we divide each term of the polynomial by this monomial to find the other factor:

20y^6 ÷ 5y^2 = 4y^4 -15y^4 ÷ 5y^2 = -3y^2 40y^2 ÷ 5y^2 = 8

Now, we can write the original polynomial as a product of the greatest common monomial factor and the other factor:

20y^6 − 15y^4 + 40y^2 = 5y^2(4y^4 − 3y^2 + 8)

The polynomial is now factored by its greatest common monomial factor.