What are the roots of the polynomial \(x^3-12x^2+44x-48=0\)?

I know the method of first using the Rational Roots Theorem and then using long division. In this case, 48 has 10 factors and testing out all of them **plus** their negatives seems like a lot of work. Is there a quicker way?

thelizzybeth Jun 18, 2020

#1**+2 **

Hint: Before trying to use the rational root theorem, try to test some values of x and find a pattern in their behavior.

Test values from -4 to 4 and see how the polynomial reacts. If one of the values makes the equation equal to zero, you can synthetic division to continue on with the process.

tertre Jun 18, 2020