Question

factorise xcube- 2x square -5x +6

Answer 1

Refer to the picture...

Hope it helps!!!!

Answer 2

Answer:

$x^3-2x^2-5x+6=(x-1)(x-3)(x+2)$

Step-by-step explanation:

Given : Expression $x^3-2x^2-5x+6$

To find : The factories of the expression?

Solution :

We apply hit n trial,

Put n=1

$x^3-2x^2-5x+6$

$(1)^3-2(1)^2-5(1)+6$

$1-2-5+6$

$-6+6=0$

Which means (x-1) is one of the factor of the expression.

Now, we divide $x^3-2x^2-5x+6$ by (x-1)

Divisor is (x-1)

Dividend is $x^3-2x^2-5x+6$

As Dividend = Divisor × Quotient +remainder

We get, Quotient $x^2-x-6$

Remainder = 0

Now, Factories further quotient

$x^2-x-6=0$

Apply middle term split,

$x^2-3x+2x-6=0$

$x(x-3)+2(x-3)=0$

$(x-3)(x+2)=0$

So, The factors of the expression is

$x^3-2x^2-5x+6=(x-1)(x-3)(x+2)$