Question

Answer 1

`a, = x^2(x-3) - 4(x-3)

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

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

`b, x^2(x-5) - 9(x - 5)`

`=(x-5)(x^2-9)`

`=(x-5)(x-3)(x+3)`

`,c, = x^2(x+7) - 4(x+7)`

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

`d, = x^3(x+1) + (x+1)`

`= (x^3+1)(x+1)`

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

Answer 2

\(1,=x^2\left(x-3\right)-4\left(x-3\right)\\ =\left(x^2-4\right)\left(x-3\right)\\ =\left(x-2\right)\left(x+2\right)\left(x-3\right)\\ b,=x^2\left(x-5\right)-9\left(x-5\right)\\ =\left(x^2-9\right)\left(x-5\right)\\ =\left(x-3\right)\left(x+3\right)\left(x-5\right)\\ 3,x^2\left(x+7\right)-4\left(x+7\right)=\left(x^2-4\right)\left(x+7\right)\\ =\left(x-2\right)\left(x+2\right)\left(x+7\right)\\ 4,x^3\left(x+1\right)+\left(x+1\right)=\left(x^3+1\right)\left(x+1\right)\\ =\left(x+1\right)^2\left(x^2+x+1\right)\)

Answer 3

1: \(=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)

2: \(=x^2\left(x-5\right)-9\left(x-5\right)=\left(x-5\right)\left(x-3\right)\left(x+3\right)\)

3: \(=x^2\left(x+7\right)-4\left(x+7\right)=\left(x+7\right)\left(x+2\right)\left(x-2\right)\)

Answer 4

1) \(x^3-3x^2-4x+12=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)

2) \(45+x^3-5x^2-9x=x^2\left(x-5\right)-9\left(x-5\right)=\left(x-3\right)\left(x+3\right)\left(x-5\right)\)

3) \(x^3+7x^2-4x-28=x^2\left(x+7\right)-4\left(x+7\right)=\left(x-2\right)\left(x+2\right)\left(x+7\right)\)

4) \(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x^3+1\right)\left(x+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)