Question

Factorise x^3 - 6x^2 - 2x + 12​

Answer 1

ANSWER:

• Factorisation of the above expression is (x-6)(x+√2)(x-√2)

GIVEN:

• x³-6x²-2x+12

TO FIND:

• Factorise the above expression.

SOLUTION:

= x³-6x²-2x+12

= (x³-6x²)+(-2x+12)

= x²(x-6) -2(x-6)

= (x-6)(x²-2)

This can be factorise again:

= (x-6)[(x)²-(√2)²]

= (x-6)(x+√2)(x-√2)

Factorisation of the above expression is (x-6)(x+√2)(x-√2)

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab