#### (i) x^{3} + x + 2

Above terms can be written as,

x^{3} + x + 1 + 1

Rearranging the above terms, we get

(x^{3} + 1) (x + 1)

(x^{3} + 1^{3}) (x + 1)

We know that, a^{3} + b^{3} = (a + b) (a^{2} – ab + b^{2})

[(x + 1) (x^{2} – x + 1)] + (x + 1)

(x + 1) (x^{2} – x + 1 + 1)

(x + 1) (x^{2} – x + 2)

##### (ii) a^{3} – a – 120

Above terms can be written as,

a^{3} – a – 125 + 5

Rearranging the above terms, we get

a^{3} – 125 – a + 5

(a^{3} – 125) – (a – 5)

(a^{3} – 5^{3}) – (a – 5)

We know that, a^{3} – b^{3} = (a – b) (a^{2} + ab + b^{2})

[(a – 5) (a^{2} + 5a + 5^{2})] – (a – 5)

(a – 5) (a^{2} + 5a + 25) – (a – 5)

(a – 5) (a^{2} + 5a + 25 – 1)

(a – 5) (a^{2} + 5a + 24)

**More Solutions:**

- Factorisation of p4 – 81² is
- Factorisation of x²- 4x-12 is
- The factorization of 4x² 8xr +3 is
- Factorisation of r2 – 4xy + 4y2 is
- Factorise 15(2x – 3)3 – 10(2x – 3)
- Factorise 2a2x – bx + 2a2 – b
- Factorise (x2 – y2)z + (y2 – z2)x
- Factorise b(c -d)2 + a(d – c) + 3c – 3d
- Factorise x(x + z) – y (y + z)
- Factorise 9×2 + 12x + 4 – 16y2