Find the division of the following by synthet | vedclass

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(A) To divide $p(x) = x^{4} - a^{4}$ by $x - a$ using synthetic division:$1$. The coefficients of $p(x) = 1x^{4} + 0x^{3} + 0x^{2} + 0x - a^{4}$ are $

Vedclass · Accepted Answer

Quotient: $x^{3} + ax^{2} + a^{2}x + a^{3}$,Remainder: $0$

Vedclass · Answer

(A) To divide $p(x) = x^{4} - a^{4}$ by $x - a$ using synthetic division:$1$. The coefficients of $p(x) = 1x^{4} + 0x^{3} + 0x^{2} + 0x - a^{4}$ are $1, 0, 0, 0, -a^{4}$.$2$. The divisor is $x - a$,so we use $a$ for synthetic division.$3$. Setting up the synthetic division table:$a$ | $1$  $0$  $0$  $0$  $-a^{4}$|    $a$  $a^{2}$  $a^{3}$  $a^{4}$---------------------------$1$  $a$  $a^{2}$  $a^{3}$  $0$$4$. The quotient coefficients are $1, a, a^{2}, a^{3}$,which corresponds to the polynomial $x^{3} + ax^{2} + a^{2}x + a^{3}$.$5$. The remainder is $0$.

Find the division of the following by synthetic division method: $p(x) = x^{4} - a^{4}$ by $x - a$.

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