Factor completely: 10y^2 - 55y + 70.
A5(y+2)(2y+7)
B5(y-7)(2y-2)
C5(y-2)(2y-7)
D5(y-14)(2y-1)
Answer & Solution
Correct answer: C. 5(y-2)(2y-7)
1. Factor out the GCF first: 10y squared - 55y + 70 has a common factor of 5, giving 5(2y squared - 11y + 14).
2. Inside the parentheses, multiply a and c: 2 times 14 equals 28.
3. Find two numbers that multiply to 28 and add to -11: -4 and -7 work.
4. Split and group: 2y squared - 4y - 7y + 14 becomes 2y(y - 2) - 7(y - 2), which factors to (y - 2)(2y - 7).
5. The complete factorization is 5(y - 2)(2y - 7), and checking by multiplying confirms it expands back to 10y squared - 55y + 70.
_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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