Question

what is the completely factored form of $x^{4}y - 4x^{2}y - 5y$?○ $y(x^{2}-5)(x^{2}+1)$○ $y(x^{2}+5)(x^{2}-1)$○ $(x^{2}y - 5)(x^{2}+1)$○ $(x^{2}y + 5)(x^{2}-1)$done

Explanation:

Step1: Factor out common term

$x^4y - 4x^2y - 5y = y(x^4 - 4x^2 - 5)$

Step2: Substitute $z=x^2$

Let $z=x^2$, so $x^4 - 4x^2 - 5 = z^2 - 4z - 5$

Step3: Factor quadratic in $z$

$z^2 - 4z - 5 = (z - 5)(z + 1)$

Step4: Substitute back $z=x^2$

$(z - 5)(z + 1) = (x^2 - 5)(x^2 + 1)$

Step5: Combine with factored $y$

$y(x^4 - 4x^2 - 5) = y(x^2 - 5)(x^2 + 1)$

Answer:

$y(x^2 - 5)(x^2 + 1)$ (Option 1)