Question

Factorize the following polynomial. (x2 – 6x – 8) (x2 – 6x – 4) – 77​

Answer 1

Answer:

$= ( {x}^{2} - 6x + 3)( {x}^{2} - 6x - 15)$

Step-by-step explanation:

$( {x}^{2} - 6x - 8)( {x}^{2} - 6x - 4) - 77 \\ \\ let \: \: {x}^{2} - 6x = y \\ \\ therefore \: \: \: \: \: (y - 8)(y - 4) - 77 = {y}^{2} - 12y + 32 - 77 \\ \\ = {y}^{2} - 12y - 45 \\ \\ = {y}^{2} - 15y + 3y - 45 \\ \\ = y(y - 15) + 3(y - 15) \\ \\ = (y + 3)(y - 15) \\ \\ = ( {x}^{2} - 6x + 3)( {x}^{2} - 6x - 15)$