Question

Factorise: x
3 − x
2 − 14x + 24.

Answer 1

Answer

Correct option is

A

(x−2)(x−12)

In the given polynomial x  

2

−14x+24,

The first term is x  

2

 and its coefficient is 1.

The middle term is −14x and its coefficient is −14.

The last term is a constant term 24.

Multiply the coefficient of the first term by the constant 1×24=24.

We now find the factor of 24 whose sum equals the coefficient of the middle term, which is −14 and then factorize the polynomial x  

2

−14x+24 as shown below:

 

x  

2

−14x+24

=x  

2

−12x−2x+24  

=x(x−12)−2(x−12)

=(x−2)(x−12)

Hence, x  

2

−14x+24=(x−2)(x−12).