Please help solve the following: x^2+6x-18/x+8x-17 y^4-12y^3-4y^2/-4y^2 4x^3-17x-17/2x-5  

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crmhaske eNotes educator| Certified Educator

The second expression is easily solved by dividing each term by `-4y^2`

`(y^4-12y^3-4y^2)/(-4y^2) =(y^4)/(-4y^2) -(12y^3)/(-4y^2) -(4y^2) /(-4y^2)=-1/4y^2+3y+1`

You can also express it in vertex form:


`1/2yh=3 -gt h=6`

`-1/4(6)^2+k=1 - gtk=9+1=10`


We will use long division to solve the third expression:

        2x^2+ 5x    + 4
2x-5|4x^3+ 0x^2-17x-17


`(4x^3-17x-17)/(2x-5)=2x^2+ 5x+4+3/(2x-5)`

The 4th expression can also be solved using long division.

As for the first expression, neither the numerator nor the denominator can be factored in such a way as to simplify the expression, and as such, writing it in a different form is a fruitless exercise.

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