If the polynomials ax^3 + 4x^2 + 3x - 4 and x | vedclass

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(C) Let $p(x) = ax^3 + 4x^2 + 3x - 4$ and $q(x) = x^3 - 4x + a$.According to the Remainder Theorem,when a polynomial $f(x)$ is divided by $x - c$,the

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$-1$

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(C) Let $p(x) = ax^3 + 4x^2 + 3x - 4$ and $q(x) = x^3 - 4x + a$.According to the Remainder Theorem,when a polynomial $f(x)$ is divided by $x - c$,the remainder is $f(c)$.Here,$c = 3$. Therefore,the remainder for $p(x)$ is $p(3)$ and for $q(x)$ is $q(3)$.$p(3) = a(3)^3 + 4(3)^2 + 3(3) - 4 = 27a + 36 + 9 - 4 = 27a + 41$.$q(3) = (3)^3 - 4(3) + a = 27 - 12 + a = 15 + a$.Since the remainders are equal,$p(3) = q(3)$.$27a + 41 = 15 + a$.$27a - a = 15 - 41$.$26a = -26$.$a = -1$.

If the polynomials $ax^3 + 4x^2 + 3x - 4$ and $x^3 - 4x + a$ leave the same remainder when each is divided by $x - 3$,find the value of $a$.

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