Use long division and divided (2x^5-15x^3-2x^2+10x-24) by (x^2-x-4)

Answer:[tex]2x^5-15x^3-2x^2+10x-24=(x^2-x-4)(2x^3+2x^2-5x+1)+(-9x-20)[/tex]Step-by-step explanation:Use long division and divided [tex](2x^5-15x^3-2x^2+10x-24)[/tex] by [tex](x^2-x-4).[/tex]1. Multiply [tex](x^2-x-4)[/tex] by [tex]2x^3[/tex] and subtract the result from  [tex](2x^5-15x^3-2x^2+10x-24):[/tex][tex]2x^5-15x^3-2x^2+10x-24-2x^3(x^2-x-4)=\\ \\=2x^5-15x^3-2x^2+10x-24-2x^5+2x^4+8x^3=\\ \\=2x^4-7x^3-2x^2+10x-24[/tex]2. Multiply [tex](x^2-x-4)[/tex] by [tex]2x^2[/tex] and subtract the result from  [tex](2x^4-7x^3-2x^2+10x-24):[/tex][tex]2x^4-7x^3-2x^2+10x-24-2x^2(x^2-x-4)=\\ \\=2x^4-7x^3-2x^2+10x-24-2x^4+2x^3+8x^2=\\ \\=-5x^3+6x^2+10x-24[/tex]3. Multiply [tex](x^2-x-4)[/tex] by [tex]-5x[/tex] and subtract the result from  [tex](-5x^3+6x^2+10x-24):[/tex][tex]-5x^3+6x^2+10x-24-(-5x)(x^2-x-4)=\\ \\=-5x^3+6x^2+10x-24+5x^3-5x^2-20x=\\ \\=x^2-10x-24[/tex]4. Multiply [tex](x^2-x-4)[/tex] by [tex]1[/tex] and subtract the result from  [tex](x^2-10x-24):[/tex][tex]x^2-10x-24-1\cdot (x^2-x-4)=\\ \\=x^2-10x-24-x^2+x+4=\\ \\=-9x-20[/tex]5. The result of the long division is[tex]2x^5-15x^3-2x^2+10x-24=(x^2-x-4)(2x^3+2x^2-5x+1)+(-9x-20)[/tex]