Question

Given the binomials (x - 2), (x - 1), (x + 2), and (x - 4), which one is a factor of f(x) = x3 + 7x2 + 14x + 8?

Answer 1

We will use the Reminder theorem.
The polynomial f ( x ) is divisible by x - a when f ( a ) = 0.
For the 1st one:
f ( - 2 ) = ( - 2 )³ + 7 · ( - 2 )² + 14 · ( - 2 ) + 8 =
= - 8 + 28 - 28 + 8 = 0
For the 2nd one:
f ( 5 )  = 3 · 5³ - 12 · 5² - 4 · 5 - 55 =
= 375 - 300 - 20 - 55 = 375 - 375 = 0
Answer;
1.  ( x + 2 )
2.  ( x - 5 )