Factor: 3u^2 + 8u + 5.
A(u+1)(3u+5)
B(u+5)(3u+1)
C(u-1)(3u-5)
D(u-5)(3u-1)
Answer & Solution
Correct answer: A. (u+1)(3u+5)
1. Multiply a and c: 3 times 5 equals 15.
2. Find two numbers that multiply to 15 and add to 8: 3 and 5 work, since 3 times 5 is 15 and 3 plus 5 is 8.
3. Split the middle term using 3u and 5u, then group: 3u squared + 3u + 5u + 5 becomes 3u(u + 1) + 5(u + 1).
4. Factor out the shared binomial (u + 1) to get (u + 1)(3u + 5).
5. Check by multiplying: 3u squared + 5u + 3u + 5 gives back 3u squared + 8u + 5.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_
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