We are asked to find unknown or the missing number to complete the polynomial given in the problem which is x² + ?x -49. First, let us equate the number to be equal to zero such as it would become x² + ?x - 49 = 0. Next, we need to find the factors such that it would produce a difference of squares and these two factors are a = +7 and b = -7. Hence, the complete solution is shown below:
(x + 7) (x-7) = 0
perform distribution and multiplication of terms such as shown below:
x² + 7x - 7x - 49 = 0
Combine the same term such as we can either add or subtract +7x to -7x and the result will be equal to 0x.
x² + 0x - 49 = 0
Therefore, the missing number is 0. The answer is 0 which will result to x² +0x - 49.