the polynomials (2x cube + x square - ax + 2) and (2x cube - 3x square - 3x + a) when divided by (x-2) leave the same remainder.find the value of a.
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Acc. to remainder theorem
x-2= g (x)
putting x=2 in 2x^3+x^2-ax+2
=2×(2)^3+(2)^2-a×2+2
=2×8+4-2a+2
=22-2a................eq 1
putting x=2 in next polynomial
=2× (2)^3-3× (2)^2-3×(2)+a
=2×8-3×4-6+a
=16-12-6+a
=a-2....................eq 2
Now
22-2a=a-2
22+2=2a+a
24=3a
24/3=a
8=a
x-2= g (x)
putting x=2 in 2x^3+x^2-ax+2
=2×(2)^3+(2)^2-a×2+2
=2×8+4-2a+2
=22-2a................eq 1
putting x=2 in next polynomial
=2× (2)^3-3× (2)^2-3×(2)+a
=2×8-3×4-6+a
=16-12-6+a
=a-2....................eq 2
Now
22-2a=a-2
22+2=2a+a
24=3a
24/3=a
8=a
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