To factor the polynomial [tex]\( 3y^4 - 2y^2 - 5 \)[/tex] completely, we will break down the expression into its simplest factors.
Let's begin by factoring it step-by-step:
1. Identify the polynomial:
[tex]\( 3y^4 - 2y^2 - 5 \)[/tex]
2. Set it in standard polynomial form:
This polynomial is already in standard form: [tex]\( ay^4 + by^2 + c \)[/tex]
3. Factor the polynomial:
[tex]\[ 3y^4 - 2y^2 - 5 \][/tex]
After factoring, we get:
[tex]\[ (y^2 + 1)(3y^2 - 5) \][/tex]
Therefore, the completely factored form of [tex]\( 3y^4 - 2y^2 - 5 \)[/tex] is:
[tex]\[
(y^2 + 1)(3y^2 - 5)
\][/tex]
Now, place the factors in the proper locations on the grid:
1. Drag (, "y", "^", "2", "+", "1", ")" to form the factor [tex]\( (y^2 + 1) \)[/tex]
2. Drag (, "3", "y", "^", "2", "-", "5", ")" to form the factor [tex]\( (3y^2 - 5) \)[/tex]
So, the input on the grid should appear as:
[tex]\[
\boxed{(y^2 + 1)(3y^2 - 5)}
\][/tex]
