Factor: y^2 + 17y + 60.
A(y+4)(y+15)
B(y+6)(y+10)
C(y+5)(y+12)
D(y-5)(y-12)
Answer & Solution
Correct answer: C. (y+5)(y+12)
1. Write the factors as two binomials with first terms y.
2. List factor pairs of 60 and their sums: 1,60 sums to 61; 2,30 sums to 32; 3,20 sums to 23; 4,15 sums to 19; 5,12 sums to 17; 6,10 sums to 16.
3. The pair 5 and 12 multiplies to 60 and adds to 17, matching the middle term.
4. Use 5 and 12 as the last terms to get (y + 5)(y + 12), and check: y squared + 12y + 5y + 60 gives back y squared + 17y + 60.
_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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