Solve for: (6x^4-5x^3+8x^2-x-20)\div(3x-4)

Expression: $\left( 6{x}^{4}-5{x}^{3}+8{x}^{2}-x-20 \right)\div\left( 3x-4 \right)$

Write the division as a fraction

$\frac{ 6{x}^{4}-5{x}^{3}+8{x}^{2}-x-20 }{ 3x-4 }$

Write $-5{x}^{3}$ as a difference

$\frac{ 6{x}^{4}+6{x}^{3}-11{x}^{3}+8{x}^{2}-x-20 }{ 3x-4 }$

Write $8{x}^{2}$ as a sum

$\frac{ 6{x}^{4}+6{x}^{3}-11{x}^{3}-11{x}^{2}+19{x}^{2}-x-20 }{ 3x-4 }$

Write $-x$ as a difference

$\frac{ 6{x}^{4}+6{x}^{3}-11{x}^{3}-11{x}^{2}+19{x}^{2}+19x-20x-20 }{ 3x-4 }$

Factor out $6{x}^{3}$ from the expression

$\frac{ 6{x}^{3} \times \left( x+1 \right)-11{x}^{3}-11{x}^{2}+19{x}^{2}+19x-20x-20 }{ 3x-4 }$

Factor out $-11{x}^{2}$ from the expression

$\frac{ 6{x}^{3} \times \left( x+1 \right)-11{x}^{2} \times \left( x+1 \right)+19{x}^{2}+19x-20x-20 }{ 3x-4 }$

Factor out $19x$ from the expression

$\frac{ 6{x}^{3} \times \left( x+1 \right)-11{x}^{2} \times \left( x+1 \right)+19x \times \left( x+1 \right)-20x-20 }{ 3x-4 }$

Factor out $-20$ from the expression

$\frac{ 6{x}^{3} \times \left( x+1 \right)-11{x}^{2} \times \left( x+1 \right)+19x \times \left( x+1 \right)-20\left( x+1 \right) }{ 3x-4 }$

Factor out $x+1$ from the expression

$\frac{ \left( x+1 \right) \times \left( 6{x}^{3}-11{x}^{2}+19x-20 \right) }{ 3x-4 }$

Write $-11{x}^{2}$ as a difference

$\frac{ \left( x+1 \right) \times \left( 6{x}^{3}-8{x}^{2}-3{x}^{2}+19x-20 \right) }{ 3x-4 }$

Write $19x$ as a sum

$\frac{ \left( x+1 \right) \times \left( 6{x}^{3}-8{x}^{2}-3{x}^{2}+4x+15x-20 \right) }{ 3x-4 }$

Factor out $2{x}^{2}$ from the expression

$\frac{ \left( x+1 \right) \times \left( 2{x}^{2} \times \left( 3x-4 \right)-3{x}^{2}+4x+15x-20 \right) }{ 3x-4 }$

Factor out $-x$ from the expression

$\frac{ \left( x+1 \right) \times \left( 2{x}^{2} \times \left( 3x-4 \right)-x \times \left( 3x-4 \right)+15x-20 \right) }{ 3x-4 }$

Factor out $5$ from the expression

$\frac{ \left( x+1 \right) \times \left( 2{x}^{2} \times \left( 3x-4 \right)-x \times \left( 3x-4 \right)+5\left( 3x-4 \right) \right) }{ 3x-4 }$

Factor out $3x-4$ from the expression

$\frac{ \left( x+1 \right) \times \left( 3x-4 \right) \times \left( 2{x}^{2}-x+5 \right) }{ 3x-4 }$

Cancel out the common factor $3x-4$

$\left( x+1 \right) \times \left( 2{x}^{2}-x+5 \right)$

Simplify the expression

$2{x}^{3}-{x}^{2}+5x+2{x}^{2}-x+5$

Collect like terms

$2{x}^{3}+{x}^{2}+5x-x+5$

Collect like terms

$2{x}^{3}+{x}^{2}+4x+5$