SOLUTION: Given that x – p is a factor of the expression x^2-(p+2)x-p^2+4p+8 , calculate the possible values of p.

Algebra ->  Equations -> SOLUTION: Given that x – p is a factor of the expression x^2-(p+2)x-p^2+4p+8 , calculate the possible values of p.      Log On


   

Question 695485: Given that x – p is a factor of the expression x^2-(p+2)x-p^2+4p+8 , calculate the possible values of p.
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
Let +f%28x%29=x%5E2-%28p%2B2%29x-p%5E2%2B4p%2B8+
By the remainder theorem +x-p+ is a factor of +f%28x%29+ if and only if +f%28p%29=0+
So +f%28p%29=0+ implies:
+p%5E2-%28p%2B2%29p-p%5E2%2B4p%2B8++=+0+
+p%5E2+-+p%5E2+-+2p+-p%5E2+%2B+4p+%2B+8++=+0+
+2p+-p%5E2+%2B+8++=+0+
+p%5E2+-2p+-8+=+0+
+%28p-4%29%28p%2B2%29+=+0+
Giving +p=4+ or +p=-2+
Check:
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When p=4 we expect +x-4+ to be a factor:

so +x-4+ is a factor
When p=-2 we expect +x-%28-2%29+=+x%2B2+ to be a factor:

so +x%2B2+ is a factor