10. If (x+4) is a factor of -x2 -11x - w = 0, then the value of w is:
a. -60
b. -28
c. 28
d. 60
To find the value of w, we need to use the factor theorem, which states that if (x + k) is a factor of a polynomial equation, then substituting -k for x will make the equation equal to zero.
In this case, we are given that (x+4) is a factor of the equation -x^2 -11x - w = 0.
So, let's substitute -4 for x:
-(-4)^2 - 11(-4) - w = 0
-16 + 44 - w = 0
28 - w = 0
To solve for w, we can add w to both sides of the equation:
28 - w + w = 0 + w
28 = w
Therefore, the value of w is 28.
So, the correct answer is c. 28.