Question

. Factorise: (i) 6x

3 – 5x

2 – √3x + 12​

Answer 1

Answer:

Consider the given that 6x

3

−5x

2

−13x+12

Put x=1 and we get,

6(1)

3

−5(1)

2

−13(1)+12

=6−5−13+12=0

Then, x=1 and x−1=0 is a factor.

Now figure above

6x

3

−5x

2

−13x+12=(x−1)(6x

2

+x−12)=0

⇒(x−1)(6x

2

+x−12)=0

⇒(x−1)(6x

2

+(9−8)x−12)=0

⇒(x−1)(6x

2

+9x−8x−12)=0

⇒(x−1)[3x(2x+3)−4(2x+3)]=0

⇒(x−1)(3x−4)(2x+3)=0

If x−1=0 then x=1

If 3x−4=0 then x=

3

4

If 2x+3=0 then x=

2

−3

Hence, the factor is 1,−

2

3

and

3

4

.