Help me on this pls!!!!!!
1 answer:
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Answer:
-1
Step-by-step explanation:
See the attachment for the polynomial long division. The constant in the quotient is -1.
_____
Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.
That could be a first guess in a "guess and check" solution approach.
<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).
<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2
Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.
Note that if 
, then 
, and so we can collapse the system of ODEs into a linear ODE:
which is a pretty standard linear ODE with constant coefficients. We have characteristic equation
so that the characteristic solution is
Now let's suppose the particular solution is
. Then
and so
Thus the general solution for
is
and you can find the solution
by simply differentiating .
which is a pretty standard linear ODE with constant coefficients. We have characteristic equation
so that the characteristic solution is
Now let's suppose the particular solution is
and so
Thus the general solution for
and you can find the solution