x^3 + 2x^2 + px -3 is divided by x+1 the remainder is the same as when it is divided by x-2. find value of p
thanks
Hello,
Let y be the common remainder. y will be a constant, because you divide by a polynom of degree 1.
If you develop , you get, by identification :
(i leave you the right to do the calculus )
In the same way,
Hence 2c'=-c.
With (1) and (2), we can state that 2(p+8)=-(p-1)
And then, just solve for p
Let P(x) and Q(x) be polynomials and k be the root of Q(x)=0.
Then the remainder of the division P(x)/Q(x) is equal to P(k).
In your question,
and
The root of Q(x) = 0 is,
,
So find P(-1),
Now find the remainder for
The root of is,
,
So
Since the remainders are the same,
To streamline things a bit ......
Use the remainder theorem:
Let the remainder be r. Then:
-1 + 2 - p - 3 = r => -2 - p = r .... (1)
8 + 8 + 2p - 3 = r => 13 + 2p = r .... (2)
Equate (1) and (2): -2 - p = 13 + 2p => p = -5.