Using rational zero theorem find all rational zeros
P(x)=3x^3+43x^2+43x+27
Factors: 27, -1, 3, 9, 27
Factors: 3, -1, 3
+-1/3, +-1, +-3, +-9, +-27 possible rational zero for function P(x)
Is this correct?
Hmm I never heard of ration zero theorem but google says it involves synthetic division and checking for roots that make the equation equal to 0? Well, errm I hate synthetic division since it requires to much guess work >.< but all of the roots you wrote down are wrong according to my calculator.
To find the possible rational zeros using the Rational Zero Theorem, you need to look at the factors of the constant term (27) and the leading coefficient (3) of the polynomial.
The constant term of the polynomial is 27, and the factors of 27 are ±1, ±3, ±9, and ±27. The leading coefficient is 3, so the possible rational zeros can be obtained by taking the factor pairs of 27 divided by the factor pairs of 3.
The possible rational zeros are then obtained by taking the ratio of the factors. In this case, the possible rational zeros are ±1/3, ±1, ±3, ±9, and ±27.
Next, you would need to use these possible rational zeros and apply a method like synthetic division or long division to check which of these zeros are actual zeros of the polynomial.