Please, use " ^ " to denote exponentiation:
f(x) = x^3 + 2x^2 − x − 2
Also, please separate your answer choices with a comma or semicolon, or put each on a new line by itself:
x − 2
x + 2
x + 3
x − 3
The easiest way to choose the correct linear expression is to use synthetic division. If you do this, and find that you have no remainder, then you know that a particular divisor in synth. div. is a root, which leads to a factor.
Look at x-2. This is a possible factor. The associated possible root is 2. Use 2 as the divisor in synth. div.:
______________
2 / 1 2 -1 -2
2 8 14
--------------- -----
1 4 7 12 Since there is a non-zero remainder, we conclude that 2 is not a root and (x-2) is not a factor.
You could also use long division and carry on until you find a possible factor for which the remainder is zero.
