Question

For what value of d is (2x - 3)(x + d) equivalent to 2x + 5x - 12? d =

Answer 1

For this case we have the following expression:

`(2x-3) (x + d) =`

Applying distributive property we have:

`2x ^ 2 + 2dx-3x-3d`

This last expression must be equivalent to:

`2x ^ 2 + 5x-12`

So, matching we have:

`2x ^ 2 + 2dx-3x-3d = 2x ^ 2 + 5x-12`

Matching similar terms we have:

`2dx-3x = 5x\\(2d-3) x = 5x\\2d-3 = 5\\2d = 5 + 3\\2d = 8\\d = \frac {8} {2} = 4`

Thus, the value of d is 4. We verify:

`(2x-3) (x + 4) = 2x ^ 2 + 8x-3x-12 = 2x ^ 2 + 5x-12`

Answer:

`d = 4`