Question

Question
(a) Use factor theorem to factorise 6x3 + 17x2 + 4x - 12 completely.​

Answer 1

Step-by-step explanation:

Given Use factor theorem to factorise 6x3 + 17x2 + 4x - 12 completely.

Now let us find whether (x + 2) is a factor.

• So we have f(x) = 6x^3 + 17x^2 + 4x – 12
•           So   f(-2) = 6(- 2)^3 + 17 (-2)^2 + 4(-2) – 12
•                            = - 48 + 68 – 8 – 12
•                               = 68 – 68
•                                = 0
• Dividing by (x + 2) we get  
•         So   x + 2) 6x^3 + 17 x^2 + 4x – 12 (6x^2 + 5x – 6
•                           6x^3 + 12x^2
•                   ------------------------------------------------------------
•                                        5x^2 + 4x – 12
•                                        5x^2 + 10x  
•                          -----------------------------------------------
•                                                 -6x – 12
•                                                 -6x – 12
•                               ------------------------------------------
•                                                       0
• So factors of  f(x) are
•    (x + 2) (6x^2 + 5x – 6)
•    (x + 2) (6x^2 + 9x – 4x – 6)
•     (x + 2) (3x(2x + 3) – 2(2x + 3)

    (x + 2) (2x + 3) (3x – 2) are the factors.

Reference link will be

https://brainly.in/question/15740265