Final answer:
The student's question is to find a value of x that makes the expression (x+4)(x-1)(3x+7) equal to zero. By setting each factor equal to zero, we find the roots of the expression, which are x = -4, x = 1, and x = -7/3. Therefore, one value of x for which the expression equals zero is -4.
Step-by-step explanation:
The student is asking for a value of x that makes the expression (x+4)(x-1)(3x+7) equal to zero. This problem involves finding the roots of a cubic polynomial. The roots of a polynomial are values of x that make the polynomial equals zero. In this case, we can find the roots by setting each factor in the expression equal to zero.
To find the roots, we set each factor equal to one of the following:
- x + 4 = 0, which gives x = -4
- x - 1 = 0, which gives x = 1
- 3x + 7 = 0, which gives x = -7/3
Therefore, one value of x for which the expression equals zero is -4, but there are actually three values in total: -4, 1, and -7/3.