Question

factorise 6x^3-25x^2+32x-12

Answer 1

6x³-25x²+32x-12=0

let x = 2
6(8)-25(4)+32(2)-12=0
48-100+64-12=0
-52+64-12=0
0=0
so (x-2) is a factor now divide it by fx

Answer 2

$\textbf{\huge\underline{\underline\red{Solution} : - }} \\ \\ \bold{ \underline\red{let }} \\ \\\bold{\purple {f(x ) =6{x}^{3} - 25 {x}^{2} + 32x - 12 }} \\ \\ \bold{ \underline\red {now \: take \: x \: = \: 2}} \\ \bold{ \underline\red{so}} \\ \\\bold{\purple {f(x = 2) =6{(2)}^{3} - 25 {(2)}^{2} + 32(2) - 12 }} \\ \\\bold{\purple {f(x = 2) =6(8) - 25 (4) + 64 - 12 }} \\ \\\bold{\purple {f(x = 2) =48 - 100 + 52 }} \\ \\\bold{\purple {f(x = 2) = - 52 + 52 }} \\ \\ \bold{\purple {f(x = 2) = 0 }} \\ \\ \bold{ \underline\blue{on \: puting \: x \: = \: 2 \: \:we \: get \: f(x) = \: 0} }\\ \bold{ \underline\blue{hence \: one \: of \: the \: factor \: of \: given \: }} \\ \bold{ \underline\blue{polynomial \: is \: (x - 2).}} \\ \\ \bold{\underline \red{now}}\\ \\\bold{\purple { =>6{x}^{3} - 25 {x}^{2} + 32x - 12 }} \\ \\ \bold{\purple { =( x - 2)(6 {x}^{2} - 13x + 6 )}} \\ \\ \bold{\purple {=( x - 2)(6 {x}^{2} - 9x - 4x + 6 )}} \\ \\ \bold{\purple { =( x - 2)(3x(2x - 3) - 2( 2x - 3))}} \\ \\ \bold{\purple { =( x - 2)(2x- 3)( 3x - 2)}} \\ \\ \fbox{\bold{ \underline\red{i \: hope \: it \: helps \: you.}}}$