Given the binomials (x − 2), (x − 1), (x + 2), and (x − 4), which one is a factor of f(x) = x^3 + 7x^2 + 14x + 8?

How do I find the factors?

Question

Given the binomials (x − 2), (x − 1), (x + 2), and (x − 4), which one is a factor of f(x) = x^3 + 7x^2 + 14x + 8?

How do I find the factors?

anonymous · Answer

Polynomial division is pretty tough to write down and not talk someone through, I suggest you ask your teacher for help on this because it's important that you understand it. 
 
Testing whether a binomial is a factor of a polynomial is a lot easier. For (x-2), simply check whether f(2)=0 (i.e. it has no remainder and is a factor).

$$f(2)=2^3-7*2^2+14*2=8 \neq0 $$$$f(1)=?$$$$f(-2)=?$$$$f(4)=?$$

Does that make sense?

anonymous · Answer

Thank you. I fully understand polynomial division/long division/synthetic division. I just got confused on how am I going to find the solution. Through inputing all numbers one by one or a simpler way. Thanks, I kinda have an idea now.

anonymous · Answer

Oh that's great. If you understand polynomial division, you can just divide the polynomial by each binomial but this way is much faster. The correct answer is -2 just in case you weren't sure. Have a look at remainder theorem, it's exactly what this uses.