Hello MHF!
I have three questions that which are throwing me for a loop. While I understand some of the principals behind them, the questions themselves defy my ability to work out.
Q1:
Simplify:
(I have no idea where to begin to work this one out, or even if I have to...)
Q2:Find a quadratic equation with the roots (4+i) and (4-i).
(I have no idea where to start with this one either.......)
Q3:Use the factor theorem to determine whether (x-3) is a factor of
(I don't understand understand the Factor Theorem very well, so I find myself thoroughly lost.)
Many thanks in advance!
Well....I remember that when doing synthetic division the non-variable aspect of the divisor is used to "divide" the coefficients, but I can't remember if I am to use 3 or -3 in the place of the 'r'.
3|
1 12 0 6 27
-3 -27 81 -261
_________________
1 9 -27 87 |-234
or, 3|
1 12 0 6 27
3 45 135 423
__________________
1 15 45 141 | 450
I know that the second version's remainder coincides with the function as worked with x=3. Therefore I am guessing that the second version is correct from what I understand of synthetic division and the remainder theorem, but I just want to make sure.
Because I worked the function as f(3) and it does not equal 0, I think that means that (x-3) is not a factor, right?