Question

Answer 1

\(1,=x^2-3x-4x+12=x\left(x-3\right)-4\left(x-3\right)=\left(x-4\right)\left(x-3\right)\\ 2,=x^2+2x-7x-14=x\left(x+2\right)-7\left(x+2\right)=\left(x-7\right)\left(x+2\right)\\ 3,=4x^2+x-4x-1=x\left(4x+1\right)-\left(4x+1\right)=\left(x-1\right)\left(4x+1\right)\\ d,=\left(x^4+4x^2+4\right)-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

Answer 2

1) \(=x\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-4\right)\)

2) \(=x\left(x+2\right)-7\left(x+2\right)=\left(x+2\right)\left(x-7\right)\)

3) \(=4x\left(x-1\right)+\left(x-1\right)=\left(x-1\right)\left(4x+1\right)\)

4) \(=\left(x^4+4x^2+4\right)-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

Answer 3

`1)x^2-7x+12`

`=x^2-3x-4x+12`

`=(x^2-3x)-(4x-12)`

`=x(x-3)-4(x-3)`

`=(x-3)(x-4)`

`2)x^2-5x-14`

`=x^2-7x+2x-14`

`=(x^2-7x)+(2x-14)`

`=x(x-7)+2(x-7)`

`=(x-7)(x+2)`

`3)4x^2-3x-1`

`=4x^2+4x-x+1`

`=(4x^2-4x)+(x-1)`

`=4x(x-1)+1(x-1)`

`=(x-1)(4x+1)`

`4)x^4+4`

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

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

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