Question

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

Answer 1

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Explanation:

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)`