91Ó°ÊÓ

For the first term, \(3u^2\), the possible factorizations are: 1. \(u\) and \(3u\) For the last term, \(30\), the possible factorizations are: 1. \(1\) and \(30\) 2. \(-1\) and \(-30\) 3. \(2\) and \(15\) 4. \(-2\) and \(-15\) 5. \(3\) and \(10\) 6. \(-3\) and \(-10\) 7. \(5\) and \(6\) 8. \(-5\) and \(-6\)

Now, we'll create pairs of the possible factors, and test them to see if they produce the correct middle term. 1. \((u+1)(3u+30)\) produces a middle term of \(33u\) 2. \((u-1)(3u-30)\) produces a middle term of \(-27u\) 3. \((u+2)(3u+15)\) produces a middle term of \(21u\) 4. \((u-2)(3u-15)\) produces a middle term of \(-9u\) 5. \((u+3)(3u+10)\) produces a middle term of \(39u\) 6. \((u-3)(3u-10)\) produces a middle term of \(-3u\) 7. \((u+5)(3u+6)\) produces a middle term of \(-3u + 15u = 12u\) 8. \((u-5)(3u-6)\) produces a middle term of \(-15u + 3u = -12u\) 9. \((3u+1)(u+30)\) produces a middle term of \(93u\) 10. \((3u-1)(u-30)\) produces a middle term of \(-87u\) 11. \((3u+2)(u+15)\) produces a middle term of \(47u\) 12. \((3u-2)(u-15)\) produces a middle term of \(-33u\) 13. \((3u+3)(u+10)\) produces a middle term of \(63u\) 14. \((3u-3)(u-10)\) produces a middle term of \(-21u\) 15. \((3u+5)(u+6)\) produces a middle term of \(23u\) 16. \((3u-5)(u-6)\) produces a middle term of \(-18u\) So we can see that the correct factored form is in option 15.

The correct factored form is \((3u+5)(u+6)\). So, the factored expression for \(3u^2 - 23u + 30\) is \((3u+5)(u+6)\).