divide the polynomial (px) by polynomial (gx) and find the quotient and remainder
(px)=x³-27x²+8x+18, (gx) = x-1
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Step-by-step explanation:
Check whether p(x) is multiple of g(x) or not
(i) p(x)=x
3
+27x
2
−8x+18, g(x)=x−1
(ii) p(x)=2
2
x
3
−5
2
x
2
+7
2
,g(x)=x+1
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ANSWER
Part (1),
Consider the given polynomial p(x)=x
3
+27x
2
−8x+18 and g(x)=x−1
Let put g(x)=x−1 then
x−1=0
x=1
Put and get value of
p(x)=(1)
3
+27(1)
2
−8(1)+18
p(x)=1+27−8+18
p(x)=38
=0
Because p(x)
=0
Hence, p(x) is not multiple of g(x).
Part (2),
Consider the given polynomial p(x)=2
2
x
3
−5
2
x
2
+7
2
and g(x)=x+1
Let put g(x)=x+1 then
x+1=0
x=−1
Put and get value of
p(x)=2
2
(−1)
3
−5
2
(−1)
2
+7
2
p(x)=−2
2
+5
2
+7
2
p(x)=10
2
=0
Because p(x)
=0
Hence, p(x) is not multiple of g(x).
Hence, this is the complete solution
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