find the polynomials (2x^3+ ax^2 +3x -5) and (x^3+ x^2 -2x +a) leave the same remainder when divided by (x-2), find the value of a. Also, find the remainder in each case
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let x-2=0
then x=2
p(x)=2×2^3+a2^2+3×2-5
=16+4a+6-5
=22-5+4a
=17+4a. eq 1
now anathor.
p(2)=2^3+2^2-2×2+a
=8+4-4+a
=12-4+a
=8+a. eq 2
now equating eq 1 and 2
17+4a=8+a
=4a-a=8-17
=3a=9
=a=9÷3
=a=3
then x=2
p(x)=2×2^3+a2^2+3×2-5
=16+4a+6-5
=22-5+4a
=17+4a. eq 1
now anathor.
p(2)=2^3+2^2-2×2+a
=8+4-4+a
=12-4+a
=8+a. eq 2
now equating eq 1 and 2
17+4a=8+a
=4a-a=8-17
=3a=9
=a=9÷3
=a=3
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