Divide p(x) = x^3 + 4x^2 + 1 by (gx) = x + 1
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Answers
Answered by
1
Answer:
The division of p(x)=x
3
+4x
2
−5x+6 by g(x)=x+1 is as shown above:
Now we know that the division algorithm states that:
Dividend=(Divisor×quotient)+Remainder
Here, the dividend is x
3
+4x
2
−5x+6, the divisor is x+1, the quotient is x
2
+3x−8 and the remainder is 14, therefore,
x
3
+4x
2
−5x+6=[(x+1)(x
2
+3x−8)]+14
⇒x
3
+4x
2
−5x+6=[x(x
2
+3x−8)+1(x
2
+3x−8)]+14
⇒x
3
+4x
2
−5x+6=x
3
+3x
2
−8x+x
2
+3x−8+14
⇒x
3
+4x
2
−5x+6=x
3
+3x
2
+x
2
−8x+3x−8+14
⇒x
3
+4x
2
−5x+6=x
3
+4x
2
−5x+6
Hence, the division algorithm is verified.
Answered by
1
Answer:
(gx) =x+1=0
x=-1
x3+4x2+1
(-1)3+4(-1)2+1
-1+4+1
answer is 4
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