QuestionJuly 16, 2025

Find the quotient. (-15m^2-12mn+36n^2)/(-5m+6n)

Find the quotient. (-15m^2-12mn+36n^2)/(-5m+6n)
Find the quotient.
(-15m^2-12mn+36n^2)/(-5m+6n)

Solution
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Answer

3(m + 2n) Explanation 1. Factor the numerator The numerator -15m^2 - 12mn + 36n^2 can be factored as -3(5m^2 + 4mn - 12n^2). Further factorization gives -3(5m - 6n)(m + 2n). 2. Simplify the expression Divide the factored numerator by the denominator: \frac{-3(5m - 6n)(m + 2n)}{-5m + 6n}. Cancel out the common term (-5m + 6n).

Explanation

1. Factor the numerator<br /> The numerator $-15m^2 - 12mn + 36n^2$ can be factored as $-3(5m^2 + 4mn - 12n^2)$. Further factorization gives $-3(5m - 6n)(m + 2n)$.<br /><br />2. Simplify the expression<br /> Divide the factored numerator by the denominator: $\frac{-3(5m - 6n)(m + 2n)}{-5m + 6n}$. Cancel out the common term $(-5m + 6n)$.
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