Factor: u^2 + 11u + 24.
A(u+2)(u+12)
B(u+3)(u+8)
C(u+4)(u+6)
D(u-3)(u-8)
Answer & Solution
Correct answer: B. (u+3)(u+8)
1. Write the factors as two binomials with first terms u, since the trinomial's variable is u.
2. List factor pairs of 24 and their sums: 1 and 24 sum to 25, 2 and 12 sum to 14, 3 and 8 sum to 11, and 4 and 6 sum to 10.
3. The pair 3 and 8 multiplies to 24 and adds to 11, matching the middle term.
4. Use 3 and 8 as the last terms to get (u + 3)(u + 8), and check: u squared + 8u + 3u + 24 gives back u squared + 11u + 24.
_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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