Question 225730: Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
f(x) = x3 + 2x2 - 5x - 6
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
f(x) = x3 + 2x2 - 5x - 6
"Rational zeros theorem" gives us possible guesses as to where roots are.
"factors of constant term"/"constants of coefficient of highest power"
+- 1,2,3,5,6/1 = +- 1, 2, 3, 5, 6
Ref:
http://www.purplemath.com/modules/
Applying "synthetic division" we quickly see that:
2 is a root
therefore, we get
(x-2)(x^2+4x+3)
Now, we can apply normal factoring techniques to the right expression giving us:
(x-2)(x+3)(x+1)
Our roots are:
x = {-3,-1,2}
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