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Factoring Equations Completely?
The directions say factor the equation completely using the rational zero theorem and synthetic division, and solve for all values of x.
x^4 - 2x^3 - 13x^2 + 14x + 24 = 0
Thanks in advance. I usually can solve these types of problems, but I am a bit rusty.
1 Answer
- Anonymous1 decade agoFavorite Answer
Try factors of 24 to determine if there is a binomial (x + a) that will be a factor of your equation. The rational zero theorem means find 'a' such that:
f(a) = a^4 - 2a^3 - 13a^2 + 14a + 24 = 0
Use synthetic division when you find the binomial factor.
When you have found a binomial factor, synthetic division will result in a new polynomial of the third degree. Repeat process to find another binomial factor. Then you will have a quadratic. You know how to factor a quadratic---yes?
This factors to:
(x - 2)(x + 3)(x - 4)(x + 1) = 0
(You can check by multiplying!)
The solutions (zeroes) are: x = 2, -3, 4, -1
Check.