SOLUTION: Factor completely over the set of REAL numbers: x^4-x^3-5x^2+3x+6.

Question 252453: Factor completely over the set of REAL numbers: x^4-x^3-5x^2+3x+6.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Real answers will occur when the curve crosses over or touches the X-axis. If you put a quick sketch together, you will quickly see it never crosses the X-axis. The lowest pint is at (0,6). Since the leading coefficient is positive and the degree is 4, we know it will open up on the left and right; end behavior is positive. Since it never reaches the X-axis there are no real solution and you cannot factor this over the reals.
ANSWER: no solution for factoring over the reals.
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