Question

Select the Quotient and Remainder when $x^3-3x+4$ is divided by $x-4.$

• A. Quotient = $x^2+4x+13$
• B. Quotient = $x^2+x+4$
• C. Remainder = $56$
• D. Remainder = $13$

Answer 1

Answer: (A), (C)

The correct options are
A Quotient = $x^2+4x+13$
C Remainder = $56$

Lets divide $x^3-3x+4$ by $x-4$

$x-4)x^3-3x+4(x^2+4x+13\underset{–}{{}_{-}{x}^3\mp 4x^2}\underset{–}{4x^2-3x+4{}^{}{}_{-}4x^2\mp 16x}\underset{–}{13x+4{}^{}{}_{-}13x\mp 52}56$

Quotient $=x^2+4x+13$
Remainder $=56$