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 | College Teacher | (Level 3) Associate Educator

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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:

`-1/4(y-h)^2+k=-1/4y^2+1/2yh-1/4h^2+k=-1/4y^2+3y+1`

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

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

`-1/4(y-6)^2+10`

We will use long division to solve the third expression:

        2x^2+ 5x    + 4
2x-5|4x^3+ 0x^2-17x-17
        4x^3-10x^2
                 10x^2-17x
                 10x^2-25x
                             8x-17
                             8x-20
                                    3

Therfore:

`(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.

Sources:

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