Question

factorise 6x^3- 5x^2- 13x+12

Answer 1

6x³-5x²-13x+12
Let x=1
6-5-13+12
1-1=0
Hence x-1 is the factor of p(x)
Now. x-1 )6x³-5x²-13x+12( 6x². +x-12
6x³-6x²
- +
x²-13x
x²-1x
- +
-12x+12
-12x+12
+ -
0
(x-1)(6x²+x-12)
(x-1)(6x²+9x-8x-12)
(x-1)[3x(2x+3)-4(2x+3)]
(x-1)(2x+3)(3x-4)
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Answer 2

Answer:

$(x-1)(2x+3)(3x-4)$

Step-by-step explanation:

Given : $6x^3- 5x^2- 13x+12$

To Find: Factorize

Solution:

$6x^3- 5x^2- 13x+12$

Take (x-1) common

$(x-1)(6x^2+x-12)$

Now use middle term splitting in the second bracket

$(x-1)(6x^2+9x-8x-12)$

$(x-1)[3x(2x+3)-4(2x+3)]$

$(x-1)(2x+3)(3x-4)$

Hence the factorization of $6x^3- 5x^2- 13x+12$   is  $(x-1)(2x+3)(3x-4)$