To determine the value of the constant b when x² is a factor of the expression x² + bx + b, we can use the rules of polynomial factorization.
Since x² is a factor, this means that we can express the given polynomial as:
(x²)(Ax + B), where A and B are constants.
This means that:
x² + bx + b = x²(Ax + B).
Expanding the right side gives us:
Ax³ + Bx².
Now, if we relate this back to our original polynomial:
Comparing coefficients:
- Coefficient of
x²:1 = B - Coefficient of
x:b = 0 - Constant term:
b = 0
Thus, it follows that both b must equal 0.
Therefore, the value of b is 0.