Question

factorize it please.

Answer 1

Answer:

( x + 1 ) ( x - 2 )² ( x - 5 )

Step-by-step explanation:

Let f(x) = ( x² - 4x ) ( x² - 4x - 1 ) - 20

To find factors, we look for ways to make this zero, so we look for ways to write 20 as a product of two number that differ by 1.

Since 20 = 5 × 4, it would do to have

x² - 4x = 5  =>  x² - 4x - 5 = 0  =>  ( x - 5 ) ( x + 1 ) = 0

So ( x - 5 ) ( x + 1 ) divides f(x).

Also 20 = -4 × -5, so it would do to have

x² - 4x = -4 =>  x² - 4x + 4 = 0  =>  ( x - 2 )² = 0

So ( x - 2 )² divides f(x).

Therefore f(x) = ( x + 1 ) ( x - 2 )² ( x - 5 )