Answer:
The quotient = 2x² - 8x + 9 with remainder 5x + 24
Step-by-step explanation:
∵[tex]\frac{4x^{4}-14x^{3}-14x^{2}+110x-84}{2x^{2}+x-12}=2x^{2}+\frac{-16x^{3}+10x^{2}+110x-84}{2x^{2}+x-12 }[/tex]
[tex]\frac{-16x^{3}+10x^{2}+110x-84}{2x^{2}+x-12}=-8x+\frac{18x^{2}+14x-84}{2x^{2}+x-12}[/tex]
[tex]\frac{18x^{2}+14x-84}{2x^{2}+x-12}=9+\frac{5x+24}{2x^{2}+x-12}[/tex]
The quotient = 2x² - 8x + 9 with remainder 5x + 24
