Solve:

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- Feb 19th 2008, 04:37 PMnerdzorPolynomial Express
Solve:

- Feb 19th 2008, 04:48 PMJhevon
by the remainder theorem, we see that is a root. thus by the factor theorem, is a factor.

dividing our cubic by , we see that:

thus, we have or

Quote:

on which of these intervals is the cubic positive? - Feb 19th 2008, 04:52 PMbobak
By inspection is a factor because is a zero of the expression

then by use synthetic division

Compare coefficients of the highest order term to get a = 1 and lowest order to get c = 4 first because it is easy

by comparing the coefficient of the term with x^2 or otherwise you should easily get b = -4

for the inequality you must sketch a graph.

You know be able to tell that for large positive values of x the function will be positive, and for large negative values of x the function will be negative.

You should also know the the sign of the function can only change at a root.

you should get a graph like this. the image below.

Remember the inequality is greater than zero not greater than or equal to, don't be lazy and just write x >1