# If X+2 is the factor of P of X= ax3(read as a xcube) +bx2(read as bxsquare) +x -6 and when divided by x-2 ,leaves a reminder 4 prove that a=0, b=2

P(x) = ax3+bx2+x-6

As x+2 is factro so P(-2) =0

P(-2) = a(-2)3+b(-2)2-2-6=0

-8a+4b=8...(i)

P(2) = 4

P(2) = a(2)3+b(2)2+2-6=4

8a +4b =8..(ii)

Equation (i)  + Equation(ii)

8b=16

b=2

So, a=0

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