Factor the higher degree polynomial. Select "Prime" if the polynomial cannot be factored. \[ 4 x^{4}-16 x^{2}+15 \]

To factor the polynomial \( 4x^4 - 16x^2 + 15 \), let's start by making a substitution to make it easier. Let \( y = x^2 \). Then, the polynomial becomes \( 4y^2 - 16y + 15 \). Next, we can attempt to factor this quadratic polynomial. We need two numbers that multiply to \( 4 \times 15 = 60 \) and add up to \( -16 \). The numbers \(-10\) and \(-6\) do the trick. Now we rewrite the middle term: \[ 4y^2 - 10y - 6y + 15 \] Grouping those pairs gives: \[ 2y(2y - 5) - 3(2y - 5) \] Factoring out the common factor \( (2y - 5) \): \[ (2y - 5)(2y - 3) \] Now, substituting back \( y = x^2 \), we find: \[ (2x^2 - 5)(2x^2 - 3) \] So the factored form is: \[ (2x^2 - 5)(2x^2 - 3) \]