If x3 +1 is divided by x2 +5 then the possible degree of quotient is
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9th
Maths
Polynomials
Factorisation of Polynomial
If polynomial p(x) is divid...
MATHS
If polynomial p(x) is divided by x
2
+3x+5, the quotient polynomial and the remainder polynomials are 2x
2
+x+1 and x=3 respectively. Find P(x).
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ANSWER
We know that the division algorithm states that:
Dividend=Divisor×Quotient+Remainder
It is given that the divisor is x
2
+3x+5, the quotient is 2x
2
+x+2 and the remainder is 3. And let the dividend be p(x). Therefore, using division algorithm we have:
p(x)=[(x
2
+3x+5)(2x
2
+x+1)]+3
=[x
2
(2x
2
+x+1)+3x(2x
2
+x+1)+5(2x
2
+x+1)]+3
=2x
4
+x
3
+x
2
+6x
3
+3x
2
+3x+10x
2
+5x+5+3
=2x
4
+7x
3
+14x
2
+8x+8
Hence, the dividend p(x) is 2x
4
+7x
3
+14x
2
+8x+8.
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