The expression 2x3+ax2+bx-2 is divisible by x+2 but leaves reamainder 7 when divide by 2x-3.Determine values of a & b.  
 

let the given polynomial be .

since p(x) is divisible by (x+2), put x+2=0 ⇒x = -2

therefore 

when p(x) is divided by (2x-3), remainder = 7.

put 2x-3 = 0 ⇒x = 3/2

multiplying eq(1) by 8 and subtracting eq(2):

substitute the value of a in eq(1):

hope this helps you.

cheers!!

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