Factor: 2y^2 + 11y + 12.
A(y+3)(2y+4)
B(y+6)(2y+2)
C(y-4)(2y-3)
D(y+4)(2y+3)
Answer & Solution
Correct answer: D. (y+4)(2y+3)
1. Multiply a and c: 2 times 12 equals 24.
2. Find two numbers that multiply to 24 and add to 11: 3 and 8 work, since 3 times 8 is 24 and 3 plus 8 is 11.
3. Split the middle term using 3y and 8y, then group: 2y squared + 3y + 8y + 12 becomes y(2y + 3) + 4(2y + 3).
4. Factor out the shared binomial (2y + 3) to get (y + 4)(2y + 3).
5. Check by multiplying: 2y squared + 3y + 8y + 12 gives back 2y squared + 11y + 12.
_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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