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After factoring out the GCF from 5k^2 - 15k - 50, why does the remaining trinomial become easier to factor?
AIts constant term becomes zero once the GCF is removed
BIt stops being a trinomial once the GCF is removed
CIts middle term disappears once the GCF is removed
DIts leading coefficient becomes 1 once the GCF is removed
Answer & Solution
Correct answer: D. Its leading coefficient becomes 1 once the GCF is removed
1. Factor out the GCF from 5k squared - 15k - 50: the GCF is 5, giving 5(k squared - 3k - 10).
2. Inside the parentheses, the leading coefficient is now 1, since 5 divided out of every term.
3. A trinomial with leading coefficient 1 can be factored with the simpler undo FOIL method instead of trial and error or the ac method.
4. Find two numbers that multiply to -10 and add to -3: -5 and 2 work, giving 5(k - 5)(k + 2).
_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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