Factor: z^2 + 4z - 5.
A(z+1)(z-5)
B(z-1)(z+5)
C(z-1)(z-5)
D(z+1)(z+5)
Answer & Solution
Correct answer: B. (z-1)(z+5)
1. The last term -5 is negative, so the factors of -5 must have opposite signs.
2. Test the factor pairs of -5: 1 and -5 sum to -4, while -1 and 5 sum to 4.
3. The pair -1 and 5 adds to the middle coefficient 4, so those are the numbers to use.
4. Use -1 and 5 as the last terms to get (z - 1)(z + 5), and check: z squared + 5z - z - 5 gives back z squared + 4z - 5.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.2 Factor Quadratic Trinomials with Leading Coefficient 1_
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