Question

What is the completely factored form of x4y – 4x2y – 5y? y(x2 – 5)(x2 1) y(x2 5)(x2 – 1) (x2y – 5)(x2 1) (x2y 5)(x2 – 1)

Answer 1

y (x² + 1) (x² - 5)

Explanation:

Factorization:

Take 'y' from each term.

x⁴y - 4x²y - 5y = y[x⁴ - 4x² - 5]

Now factorize x⁴ - 4x² - 5.

Sum = -4

Product = -5

Factors = -5 , 1

When we add (-5) + 1, it gives (-4) and when we multiply (-5)*1, gives (-5).

x⁴ - 4x² - 5 = x⁴ + x² - 5x² - 5

= x²(x² + 1) -5(x² + 1)

= (x²+ 1) (x² - 5)

x⁴y - 4x²y - 5y = y (x² + 1) (x² - 5)