`c)`
`C1:`
`x²+5x+6`
`=x²+2x+3x+6`
`=(x²+2x)+(3x+6)`
`=x(x+2)+3(x+2)`
`=(x+2)(x+3)`
`C2:`
`x²+5x+6`
`=x²+5x+25/4-1/4`
`=(x²+5x+25/4)-1/4`
`=[x²+2.x. 5/2+(5/2)^2]-1/4`
`=(x+5/2)^2-(1/2)^2`
`=(x+5/2+1/2)(x+5/2-1/2)`
`=(x+6/2)(x+4/2)`
`=(x+3)(x+2)`
`d)`
`C1:`
`x²-x-6`
`=x²-3x+2x-6`
`=(x²-3x)+(2x-6)`
`=x(x-3)+2(x-3)`
`=(x-3)(x+2)`
`C2:`
`x²-x-6`
`=x²-x+1/4-25/4`
`=(x²-x+1/4)-25/4`
`=[x²-2.x. 1/2+(1/2)^2]-25/4`
`=(x-1/2)^2-(5/2)^2`
`=(x-1/2+5/2)(x-1/2-5/2)`
`=(x+4/2)(x-6/2)`
`=(x+2)(x-3)`
`e)`
`C1:`
`x²-4x+3`
`=x²-3x-x+3`
`=(x²-3x)-(x-3)`
`=x(x-3)-(x-3)`
`=(x-3)(x-1)`
`C2:`
`x²-4x+3`
`=x²-4x+4-1`
`=(x²-4x+4)-1`
`=(x²-2.x.2+2²)-1`
`=(x-2)²-1²`
`=(x-2+1)(x-2-1)`
`=(x-1)(x-3)`
`g)`
`C1:`
`2x²-5x+3`
`=2x²-2x-3x+3`
`=2x(x-1)-3(x-1)`
`=(x-1)(2x-3)`
`C2:`
`2x²-5x+3`
`=2x²-5x+5-2`
`=(2x²-2)-(5x-5)`
`=2(x²-1)-5(x-1)`
`=2(x+1)(x-1)-5(x-1)`
`=(x-1)[2(x+1)-5]`
`=(x-1)(2x+2-5)`
`=(x-1)(2x-3)`
