Question

(x²-x) (4x² - 4x - 5)-6​

Answer 1

Answer:

$(x - 2) \: (x + 1) \: (4 {x}^{2} - 4x + 3)$

Step-by-step explanation:

$\bold{Given}\longrightarrow \\ ( {x}^{2} - x) \: (4 {x}^{2} - 4x - 5) - 6$

$\bold{To \: find}\longrightarrow \\ factors \: of \: given \: expression$

$\bold{Solution}\longrightarrow \\ ( {x}^{2} - x) \: (4 {x}^{2} - 4 x - 5) - 6 \\ = ( {x}^{2} - x) \: (4( {x}^{2} - x) - 5) -6\\ let \: ( {x}^{2} - x \: ) = y \\ = y \: (4y - 5) - 6 \\ = 4 {y}^{2} - 5y - 6 \\ = 4 {y }^{2} - (8 - 3)y - 6 \\ = 4 {y}^{2} - 8y + 3y - 6 \\ = 4y(y - 2) + 3(y - 2) \\ = (y - 2) \: (4y + 3) \\ putting \: y = {x}^{2} - x \: we \: get \\ = ( {x}^{2} - x - 2) \: (4( {x}^{2} - x) + 3) \\ = ( {x}^{2} - 2x + x - 2) \: (4 {x}^{2} - 4x + 3) \\ = (x(x - 2) + 1(x - 2)) \: (4 {x}^{2} - 4x + 3) \\ = (x - 2) \: (x + 1) \: (4 {x}^{2} - 4x + 3)$

Answer 2

Step-by-step explanation:

$( {x}^{2} - x )(4 {x}^{2} - 4x - 5) - 6 \\ = ( {x}^{2} - x)4( {x}^{2} - x) - 5 - 6 \\ = y(4y - 5) - 6 \\ = 4 {y}^{2} -y (8 - 3) - 6 \\ = 4y(y - 2) + 3(y - 2) \\ = (y - 2)(4y + 3) \\ \\ \sf \: putting \: y = {x}^{2} - x \: \\ \\ ( {x}^{2} - x - 2)4( {x}^{2} - x) + 3 \\ = x(x - 2) + 1(x - 2)(4 {x}^{2} - 4x + 3) \\ = (x - 2)(x - 1)(4 {x}^{2} - 4x + 3)$