Question

Find the quotient: 15x^4y^2-30x^2y^3+45xy/5xy is ________. when this quotient is divided by _____the result is x^3y-2xy^2+3

Answer 1

$\dfrac{15x^4y^2-30x^2y^3+45xy}{5xy}=\dfrac{15x^4y^2}{5xy}-\dfrac{30x^2y^3}{5xy}+\dfrac{45xy}{5xy}\\\\=3x^{4-1}y^{2-1}-6x^{2-1}y^{3-1}+9=3x^3y-6xy^2+9\\\\=3(x^3y-2xy^2+3)\\\\Used:\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\Answer:\\....\underline{3x^3y-6xy^2+9}...\ \ \ ...\underline{3}...$