Question

factories :(2a+3)x^2 -9ax- (3-7a)​

Answer 1

$\large\underline{\sf{Solution-}}$

Given polynomial is

$\rm :\longmapsto\:(2a + 3) {x}^{2} - 9ax - (3 - 7a)$

can be rewritten as

$\rm \:  =  \: \:(2a + 3) {x}^{2} - 9ax + (7a - 3)$

Split 9a as 7a + 2a

$\rm \:  =  \: \:(2a + 3) {x}^{2} - \red{ (7a + 2a)x} + (7a - 3)$

Adding and Subtracting 3, we get

$\rm \:  =  \: \:(2a + 3) {x}^{2} - \red{ (7a + 2a + 3 - 3)x} + (7a - 3)$

$\rm \:  =  \: \:(2a + 3) {x}^{2} - \red{ \bigg[( 2a + 3) + (7a- 3)\bigg]x} + (7a - 3)$

$\rm \:  =  \: \:(2a + 3) {x}^{2} - ( 2a + 3) x - (7a- 3)x + (7a - 3)$

$\rm \:  =  \: \:(2a + 3)x\bigg[x - 1\bigg] - (7a- 3)\bigg[x - 1\bigg]$

$\rm \:  =  \: \:(x - 1)\bigg[(2a + 3)x - (7a - 3)\bigg]$

Hence,

Factorization of

$\rm :\longmapsto\:(2a + 3) {x}^{2} - 9ax - (3 - 7a)$

is

$\rm \:  =  \: \:(x - 1)\bigg[(2a + 3)x - (7a - 3)\bigg]$

Additional Information :-

$\green{ \boxed{ \sf{ \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}}$

$\green{ \boxed{ \sf{ \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}}}$

$\green{ \boxed{ \sf{ \: {(x - y)}^{3} = {x}^{3} - 3xy(x - y) - {y}^{3}}}}$

$\green{ \boxed{ \sf{ \: {(x + y)}^{3} = {x}^{3} + 3xy(x + y) + {y}^{3}}}}$