when a polynomial is divided by x-1,x+1andx+2 it leaves the reminders -1,1and2 respectively.Find the reminder when it is divided by x^3+2x^2-x-2.
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Answer:
The given polynomial is f (x) =
by remainder theorem, when f(x) is divided by (x-4),then f(4) = R1
therefore,
f(4) = 64a+48-3
f(4) = 64a+45
and g(x) =
by remainder theorem, when g(x) is divided by (x-4),then f(4) = R2
therefore,
g(4) = 128-20+a
g(4) = a+108
now,
(i) 2R1 - R2 = 0
⇒2(64a+45)-a-108 =0
⇒128a+90-a - 108=0
⇒127a = 18
⇒a = - 18/127
(ii) R1+R2=0
⇒64a+45+a+108 = 0
⇒65a+153=0
⇒a= -153/65
(iii) R1=R2
⇒64a+45 = a+108
⇒63a=63
⇒a=63/63
⇒a=1
similarly, the other parts can be solved.
Factorise each of the following :
1. 8a^3-b^3-12a^2b+6ab^2
Solution:
similarly, the other parts can be solved.
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