Divide the polynomial p(x) by the polynomial g(x) and find the quotient and reminder in each of the following:
1). p(x) =x³-3x²+5x-3, g(x)=x²-2
2). p(x) =x⁴-3x²+4x+5, g(x) =x²+1-x
3). p(x) =x⁴-5x+6, g(x) =2-x²
Answers
Answer:
Solution
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(i) x−3
x
2
−2)
x
3
−3x
2
+5x−3
x
3
−2x
________________
−3x
2
+7x−3
−3x
2
−6
________________
7x−9
Quotient=x−3
Remainder=7x−9
(ii) x
2
+x−3
x
2
−x+1)
x
4
−3x
2
+4x+5+0x
3
x
4
+x
2
−x
3
______________________
x
3
+4x
2
+4x+5
x
3
−x
2
+x
______________________
−3x
2
+3x+5
−3x
2
+3x−3
______________________
8
Quotient=x
2
+x−3
Remainder=8
(iii) −x
2
−2
2−x
2
)
x
4
+0x
3
+0x
2
−5x+6
x
4
−2x
2
____________________
0x
3
+2x
2
−5x+6
+2x
2
−4
_____________________
−5x+10
Quotient=−x
2
−2
Remainder=−5x+10.