Factor: t^2 - 11t + 28.
A(t-4)(t-7)
B(t-2)(t-14)
C(t-1)(t-28)
D(t+4)(t+7)
Answer & Solution
Correct answer: A. (t-4)(t-7)
1. The last term 28 is positive and the middle term is negative, so both numbers must be negative.
2. Find two negative numbers that multiply to 28 and add to -11.
3. The pair -4 and -7 multiplies to 28 and adds to -11.
4. Use -4 and -7 as the last terms to get (t - 4)(t - 7), and check: t squared - 7t - 4t + 28 gives back t squared - 11t + 28.
_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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