Answer:
D. 20
Step-by-step explanation:
Use long division to find k:
[tex]\phantom{x+1)x^{3}-2}x^{2}-\ 3x+16\\x+1)\overline{x^{3}-2x^{2}+13x+k}\\\phantom{x+1)}x^{3}+\ x^{2}\\\phantom{x+1)}\overline{\phantom{x^{3}}-3x^{2}}+13x\\\phantom{x+1)x^{3}}-3x^{2}-\ 3x\\\phantom{x+1)x^{3}}\overline{\phantom{-4x^{2}-\ \ }16x}+k\\\phantom{x+1)x^{3}-2x^{2}+\ }16x+16\\\phantom{x+1)x^{3}-2x^{2}-\ }\overline{\phantom{17x+\ }k-16}[/tex]
The remainder is -8, so:
k − 16 = -8
k = 8
Use long division to find the new remainder:
[tex]\phantom{x+1)x^{3}-2}x^{2}-\ \ \ x+12\\x-1)\overline{x^{3}-2x^{2}+13x+8}\\\phantom{x+1)}x^{3}-\ x^{2}\\\phantom{x+1)}\overline{\phantom{x^{3}}\ -x^{2}}+13x\\\phantom{x+1)x^{3}\ }-x^{2}+\ \ \ x\\\phantom{x+1)x^{3}}\overline{\phantom{-4x^{2}-\ \ }12x}+8\\\phantom{x+1)x^{3}-2x^{2}+\ }12x-12\\\phantom{x+1)x^{3}-2x^{2}-\ }\overline{\phantom{12x+\ }20}[/tex]
The remainder is 20.
