Question

$6x { }^{2} + 5x - 6$
​

Answer 1

Answer :

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

Step-by-step explanation :

Given quadratic equation,

6x² + 5x - 6

=> It is of the form ax² + bx + c

   a = 6, b = 5, c = -6

a - coefficient of x²

b - coefficient of x

c - constant term

By sum-product pattern,

>> Find the product of quadratic term [ax²] and constant term [c]

   = (6x²) × (-6)

   = -36x²

>> find the factors of "-36x²" in pairs

  = (x) (-36x)

  = (-x) (36x)

  = (-2x) (18x)

  = (2x) (-18x)

  = (3x) (-12x)

  = (-3x) (12x)

  = (4x) (-9x)

  = (-4x) (9x)

  = (6x) (-6x)

>> From the above, find the pair that adds to get linear term [bx]

  9x - 4x = 5x

>> Split 5x into 9x and -4x

    6x² + 5x - 6

   6x² + 9x - 4x - 6

>> Find the common factor

  3x(2x + 3) - 2(2x + 3)

   (2x + 3) (3x - 2)

6x² + 5x - 6 =  (2x + 3) (3x - 2)

Answer 2

$\huge\bf\underline\red{☆Solution☆}$

6x²+5x-6

6x² + 9x - 4x -6

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

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

So, 6x²+5x-6=(2x + 3)(3x -2)

$\huge\bf\underline\pink{☆Verification☆}$

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

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

6x² - 4x + 9x -6

6x² + 5x -6 Hence verified !!