6.
Show that (x - 1) is a factor of 2x + (p+3)x3+px2 - (p + 5) x-p for all values of p. If (x + 2) is also
a factor, find p. Find all the factors for that value of p. Thus solve f(x) = 0.
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Given polynomial x
3
−px
2
+6x−p divided by x−p
If divided by x−p then x−p=0 or x=p
Replace x by p we get
q(x)=x
3
−px
2
+6x−p
q(p)=(p)
3
−p(p)
2
+6(p)−p
⇒q(p)=p
3
−p
3
+6p−p
⇒q(p)=5p
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