Question

Answer 1

a) `x^4+x^3+x^2+x=x^3(x+1)+x(x+1)=(x+1)(x^3+x)=(x+1).x.(x^2+1)`

b) `x^3+2x^2-x-2=(x^3-x)+(2x^2-2)`

`=x(x^2-1)+2(x^2-1)`

`=(x+2)(x^2-1)`

`=(x+2)(x-1)(x+1)`

c) `x^2-xy-x+y`

`=(x^2-xy)-(x-y)`

`=x(x-y)-(x-y)`

`=(x-y)(x-1)`

d) `xy+4-x^2+2y`

`=(xy+2y)+(4-x^2)`

`=y(x+2)+(2-x)(x+2)`

`=(x+2)(y+2-x)`

e) `xy+y-2(x+1)`

`=y(x+1)-2(x+1)`

`=(x+1)(y-2)`

f) `2(x+y)+ay+ax`

`=2(x+y)+a(x+y)`

`=(x+y)(a+2)`