9514 1404 393
Answer:
-(x -3)(x +7)
Explanation:
Apparently, you're supposed to match the given expression with the parts of the identity ...
(x + a)(x + b) = x² +(a +b) +ab
First of all, we notice that the sign of x² in our given expression is negative. So, we factor -1 out of the expression first.
-x² -4x +21 = -(x² +4x -21)
Now, matching the coefficients of x, and the constant to those in our identity, we see ...
a + b = 4 . . . . . coefficients of x
ab = -21 . . . . . . constants
It is relatively easy to find the factors of -21. We are interested in those factor pairs such that the sum is positive:
-21 = -1(21) = -3(7) = -7(3) . . . . at this point the sum -7+3 becomes negative
The factor pair a=-3, b=7 will satisfy ...
a + b = -3 + 7 = 4
ab = (-3)(7) = -21
So, our factorization is ...
-x² -4x +21 = -(x² +4x -21) = -(x -3)(x +7)