Question

Solve
$(a^4-a^3+a^2-a+1)÷(a^3-2)$
and $(4x^4-5x^3-7x+1)÷(4x-1)$

Answer 1

$(a^4-a^3+a^2-a+1)÷(a^3-2)$

$a^3-2)a^4-a^3+a^2-a+1(a-1$

$a^4-2a$

$-$ $+$

___________________

$-a^3+a^2+a+1$

$-a^3+2$

$+$ $-$

____________________

$a^2+a-1$

remainder $\to a^2+a-1$

$4x-1)4x^4-5x^3-7x+1(x^3-x^2-\frac{1}{4}x-\frac{29}{16}$

$4x^4-x^3$

$-$ $+$

___________________

$-4x^3-7x+1$

$-4x^3+x^2$

$+$ $-$

___________________

$-x^2-7x+1$

$-x^2+\frac{1}{4}x$

$+$ $-$

__________________

$-\frac{29}{4}x+1$

$-\frac{29}{4}x+\frac{29}{16}$

$+$ $-$

___________________

$-\frac{13}{16}$

Remainder $=\frac{-13}{16}$