Given the expression:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}[/tex]
• You can find the Quotient by dividing the numerator by the denominator as follows:
1. Identify the Greatest Common Factor in the numerator (the largest factor that all the terms in the numerator have in common). In this case, this is:
[tex]GCF=5xy[/tex]
2. Factor the Greatest Common Factor out:
[tex]=\frac{5xy(3x^3y-6xy^2+9)}{5xy}[/tex]
3. Since:
[tex]\frac{5xy}{5xy}=1[/tex]
You get that the Quotient is:
[tex]=3x^3y-6xy^2+9[/tex]
• Given the result of dividing the Quotient obtained before by a number:
[tex]x^3y-2xy^2+3[/tex]
You can identify that the Leading Coefficient is 1 and it was 3 before the division by the number.
Since:
[tex]\frac{3}{3}=1[/tex]
You can conclude that the Quotient was simplified by dividing all its terms by 3.
Hence, the answers are:
- First option:
[tex]3x^3y-6xy^2+9[/tex]
- First option:
[tex]3[/tex]
