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Division of a Polynomial by a Monomial

the product o...

Question

the product of two polynomials is $7.5 a^{3} b^{2} - 2.5 a b + 10 a^{2} b^{2}$ . if one of them is 2.5ab,find the other polynomial.

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Solution

Product $(P) = 7.5 a^{3} b^{2} - 2.5 a b + 10 a^{2} b^{2}$
$P_{1} = 2.5 a b$
$P_{2} =$ $\frac{7.5 a^{3} b^{2} - 2.5 a b + 10 a^{2} b^{2}}{2.5 a b} = 3 a^{2} b - 1 + 4 a b$

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