Question

Complete the factorization shown. 2x2 − x − 6 = (2x + )(x − )

Answer 1

2x^2 − x − 6 = (2x + 3)(x −2 )

cause
 (2x + 3)(x −2 )
= 2x^2 − 3x  + 2x - 6
= 2x^2 − x -6

answer
 (2x + 3)(x −2 )

Answer 2

ANSWER

The complete factorization is

$2 {x}^{2} - x - 6 = (2x + 3)(x - 2)$

EXPLANATION

The given expression is

$2 {x}^{2} - x - 6$

This is a quadratic trinomial with,

$a=2,b=-1,c=-6$

$ac = - 12$


Two factors of -12 that adds up to -1 are

$- 4,3$


We split the middle term to obtain,


$2 {x}^{2} - 4x + 3x- 6$

We factor to get,

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


We factor further to get,


$\therefore2 {x}^{2} - x - 6 = (2x + 3)(x - 2)$