Question

Using factor theorem factorise 6x3 + 17x2 + 4x - 12 completely.​

Answer 1

Answer:

52+4x

Step-by-step explanation:

(6*3=18)+(17*2=34)+4x-12

18+34-12+4x

=52+4x

Answer 2

Answer:

(x+2)(2x+3)(3x-2)

Step-by-step explanation:

(x)= 6x³+17x²+4x-12.

factors of 12 are +-1;+-2;+-3;+-4;+-6;+-12.

f(-1)= 6×(-1)³+17×(-1)²+4×(-1)-12

= -6+17-4-12

= 17-22

= -5 is not equal to 0

hence x+1 is not a factor of f(x)

f(-2)= 6 × (-2)³+17×(-2)²+4×(-2)-12

= -48+68-8-12

= 68-68

= 0

hence x+2 is a factor of f(x).

•°• dividing f(x) by x+2,

x+2|6x³+17x²+4x-12|6x²+5x-6

6x³+12x²

-. -

5x²+4x-12

5x²+10x

-. -

-6x-12

-6x-12

+. +

0

[6×6=36....... LCM of 36 are 1,2,2,3,3.]*

the factors of f(x) are:-

= (x+2)(6x²+5x-6)

= (x+2)(6x²+9x-4x-6)

= (x+2)[3x(2x+3)-2(2x+3)]

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

Hope it Helps