What is (6x^2 - 8x + 8) \text{ divided } (x - 3)?

Question:

What is {eq}(6x^2 - 8x + 8) \text{ divided } (x - 3)? {/eq}

Division of polynomial functions:

To divide a polynomial expression by a monomial, the polynomial shoukd be factored out and then the like terms should be cancelled. To factor a quadratic expression, the quadratic formula can be used.

Answer and Explanation:


If we look at the quadratic expression given, using the terms used in the quadratic formula, we have a=6, b=-8, c=8. This gives:


$$\begin{align} b^2-4ac&=(-8)^2-4*6*8\\&=-128<0 \end{align} $$


What we have calculated above is the discriminant of the quadratic expression. As this is negative, it is not possible to factor the expression as it does not have any real roots.

As the expression cannot be factored, the expressions cannot be divided.


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