If the polynomial az3+az2+3z-4and z3-4z+a leave the same remainder whe

1.	If the polynomial az3+az2+3z-4and z3-4z+a leave the same remainder when divided by z-3 find a
Answer» Let p(z) = az3 + 4z2 + 3z - 4And q(z) = z3 - 4z + aAs these two polynomials leave the same remainder, when divided by z - 3, then p(3) = q(3).{tex}\\therefore{/tex} p(3) = a(3)3 + 4(3)2 + 3(3) - 4= 27a + 36 + 9 - 4Or p(3) = 27a + 41And q(3) = (3)3 - 4(3) + a= 27 - 12 + a = 15 + aNow, p(3) = q(3){tex}\\Rightarrow{/tex} 27a + 41 = 15 + a{tex}\\Rightarrow{/tex} 26a = -26; a = -1Hence, the required value of a = -1.

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