If the polynomials az^{3}+4z^{2}+3z-4 and z^{ | vedclass

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(B) Let $p(z) = az^{3} + 4z^{2} + 3z - 4$ and $q(z) = z^{3} - 4z + a$.According to the Remainder Theorem,when a polynomial $f(z)$ is divided by $(z -

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$-1$

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(B) Let $p(z) = az^{3} + 4z^{2} + 3z - 4$ and $q(z) = z^{3} - 4z + a$.According to the Remainder Theorem,when a polynomial $f(z)$ is divided by $(z - c)$,the remainder is $f(c)$.Since both polynomials leave the same remainder when divided by $z - 3$,we have $p(3) = q(3)$.First,calculate $p(3)$:$p(3) = a(3)^{3} + 4(3)^{2} + 3(3) - 4$$p(3) = 27a + 36 + 9 - 4 = 27a + 41$.Next,calculate $q(3)$:$q(3) = (3)^{3} - 4(3) + a$$q(3) = 27 - 12 + a = 15 + a$.Equating the two remainders:$27a + 41 = 15 + a$$27a - a = 15 - 41$$26a = -26$$a = -1$.Thus,the value of $a$ is $-1$.

If the polynomials $az^{3}+4z^{2}+3z-4$ and $z^{3}-4z+a$ leave the same remainder when divided by $z-3$,find the value of $a$.

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