Question

How do you factorise this equation: 2x^2+5x-12

Answer 1

Hello!

2x² + 5x - 12

= (2x² + 8x) + (-3x - 12)

= 2x(x + 4) - 3(x + 4)

= (2x -3)(x + 4)

Answer 2

`\Huge \boxed{(2x - 3)(x + 4) }`

Explanation:

Step 1:

Multiply the coefficient of the
`x^2` term (which is 2) by the constant term (which is -12):

• 
  `2 * -12 = -24`

Step 2:

Find two factors of -24 that add up to the coefficient of the
`x` term (which is 5):

-3 and 8

• 
  `-3 + 8 = 5`

Step 3:

Rewrite the middle term (5x) as the sum of the two terms found in step 2 (which are -3x and 8x):

• 
  `2x^2 - 3x + 8x - 12`

Step 4:

Group the terms into two pairs, and factor out the greatest common factor from each pair:

• 
  `(2x^2 - 3x) + (8x - 12)`

• 
  `x(2x - 3) + 4(2x - 3)`

Notice that both terms now have a common factor of
`(2x - 3)`:

• 
  `(2x - 3)(x + 4)`

Therefore, the factorisation of
`2x^2 + 5x - 12` is:

• 
  `(2x - 3)(x + 4)`

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