For this case we have the following expression:
[tex](2x-3) (x + d) =[/tex]
Applying distributive property we have:
[tex]2x ^ 2 + 2dx-3x-3d[/tex]
This last expression must be equivalent to:
[tex]2x ^ 2 + 5x-12[/tex]
So, matching we have:
[tex]2x ^ 2 + 2dx-3x-3d = 2x ^ 2 + 5x-12[/tex]
Matching similar terms we have:
[tex]2dx-3x = 5x\\(2d-3) x = 5x\\2d-3 = 5\\2d = 5 + 3\\2d = 8\\d = \frac {8} {2} = 4[/tex]
Thus, the value of d is 4. We verify:
[tex](2x-3) (x + 4) = 2x ^ 2 + 8x-3x-12 = 2x ^ 2 + 5x-12[/tex]
Answer:
[tex]d = 4[/tex]
