Question

15:4y2 – 30:23 + 4554The quotient of517is7. When this quotient is divided bythe result is 3-35-5I3y – 25y2 + 3

Answer 1

We are given the following expression:

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

To determine the quotient of the expression we will factor the numerator. To do that we take the Greatest Common Multiple of the denominator.

The denominator is the following expression:

`15x^4y^2-30x^2y^3+45xy`

To get the greatest common multiple we need to determine the multiples of the coefficients first.

For 15 we have:

`factors\text{ 15= 1, 3, 5, 15}`

For 30 we have:

`\text{factors 30 = }1,2,3,5,6,10,15,30`

For 45 we have:

`\text{factors 45 =}1,3,5,9,15,45`

We notice that the factors that are repeated for each of the numbers are:

The greatest of the repeated factors is 15, therefore, the greatest common factor is 15.

Now, we take the variables that are repeated in the expression and we take the ones with smaller exponents. The variables repeated are:

Of these, the ones with smaller exponents are:

Now, combining the two parts we get that the greatest common factor of the denominator is:

`15xy`

We take out that factor and re arrange the expression, like this:

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

Now, we cancel out the "xy" and simplify 15/5:

`(15xy(x^3y-2xy^2+3))/(5xy)=3(x^3y-2xy^2+3)`

And thus we get the quotient.

We notice that the quotient is multiplied by 3, therefore, if we divide by 3:

`(3(x^3y-2xy^2+3))/(3)`

We can cancel out the 3 and we get:

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

Therefore, the quotient is divided by 3.