Question

15x4y2 – 30x2y3 + 45xy/5xyis3(x^3)y - 6x(y^2) +93(x^3)y + 6x(y^2) - 33(x^2)y + 5x(y^2) - 93(x^3)y + 5x(y^2) + 3when this quotient is divided by3-35-5the result is X3y – 2y2 + 3

Answer 1

Given the expression:

`(15x^4y^2-30x^2y^3+45xy)/(5xy)`

• 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:

`GCF=5xy`

2. Factor the Greatest Common Factor out:

`=(5xy(3x^3y-6xy^2+9))/(5xy)`

3. Since:

`(5xy)/(5xy)=1`

You get that the Quotient is:

`=3x^3y-6xy^2+9`

• Given the result of dividing the Quotient obtained before by a number:

`x^3y-2xy^2+3`

You can identify that the Leading Coefficient is 1 and it was 3 before the division by the number.

Since:

`(3)/(3)=1`

You can conclude that the Quotient was simplified by dividing all its terms by 3.

Hence, the answers are:

- First option:

`3x^3y-6xy^2+9`

- First option:

`3`