To find the differential coefficient (derivative) of (x - 1)(2x + 5), expand the polynomial to get 2x^2 + 3x - 5, then differentiate each term to get the final answer, which is 4x + 3.
The student is asking for the differential coefficient, which is another term for the derivative, of the polynomial function (x - 1)(2x + 5). To find this, we can either apply the product rule directly or first expand the polynomial and then take its derivative.
Explanation:
- Expand the polynomial: (x - 1)(2x + 5) = 2x2 + 3x - 5.
- Find the derivative of each term individually: d/dx (2x2) = 4x, d/dx (3x) = 3, and d/dx (-5) = 0.
- Combine the derivatives of all terms to obtain the final derivative of the polynomial: 4x + 3.
So, the differential coefficient of the polynomial (x - 1)(2x + 5) is 4x + 3.