Question 260983
(I'm going to use 0.5 instead of 1/2 to make things easier for me.)
(x+0.5) is a factor of a polynomial if it divides evenly (IOW the remainder is zero) into the polynomial. So all we have to do is divide the polynomial by (x+0.5) and see if the remainder is zero:
<pre>
-0.5 |   10    9   -4   9   6
------        -5   -2   3  -6
         ---------------------
         10    4   -6  12   0
</pre>
The remainder is 0. So (x + 0.5) is a factor of P(x). (The other factor, taken from the numbers in front of the remainder, is {{{10x^3 +4x^2 -6x +12}}}