Question

Solve: $(4x^4-{5x}^3-7x+1)÷(4x-1)$

Answer 1

Evaluate the given expression by long division method as
$4x-1)4x^4-5x^3-7x+1(x^3-x^2-\frac{x}{4}-\frac{29}{16}$

$4x^4-x^3$

$-$ __$+$____________

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

$-4x^3+x^2$

$+$ ____$-$__ _________

$-x^2-7x+1$

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

$+$__$-$_______________

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

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

$+$ ____$-$__________

$-\frac{13}{16}$

Quotient: $x^3-x^2-\frac{x}{4}-\frac{29}{16}$

Remainder: $-\frac{13}{16}$.