3. Divide the polynomial
P(x)= x -3x2+2x+5 ,g(x) = x2+2x+3
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p(x)=2x
3
+x
2
−2x−1,g(x)=x+1
g(x)=0⇒x+1=0⇒x=−1
∴ Zero of g(x) is −1
Now, p(−1)=2(−1)
3
+(−1)
2
−2(−1)−1
=−2+1+2−1=0
∴ By factor theorem, g(x) is a factor of p(x).
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