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?
Stacey Warren - Expert brainly.com
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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?
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.
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.