Solve 5x^3-4x^2+7x+15-2*1x^3/2-x^2+2x+10+3*2{x}^3-3{x}^2+5x-5

$$5 { x }^{ 3 } -4 { x }^{ 2 } +7x+15-2 \times \frac{ 1 { x }^{ 3 } }{ 2 } - { x }^{ 2 } +2x+10+3 \times 2 { x }^{ 3 } -3 { x }^{ 2 } +5x-5$$

Evaluate

$$10x^{3}-8x^{2}+14x+20$$

Solution Steps

Cancel out 2 and 2.

$$5x^{3}-4x^{2}+7x+15-x^{3}-x^{2}+2x+10+3\times 2x^{3}-3x^{2}+5x-5$$

Combine 5x^{3} and -x^{3} to get 4x^{3}.

$$4x^{3}-4x^{2}+7x+15-x^{2}+2x+10+3\times 2x^{3}-3x^{2}+5x-5$$

Combine -4x^{2} and -x^{2} to get -5x^{2}.

$$4x^{3}-5x^{2}+7x+15+2x+10+3\times 2x^{3}-3x^{2}+5x-5$$

Combine 7x and 2x to get 9x.

$$4x^{3}-5x^{2}+9x+15+10+3\times 2x^{3}-3x^{2}+5x-5$$

Add 15 and 10 to get 25.

$$4x^{3}-5x^{2}+9x+25+3\times 2x^{3}-3x^{2}+5x-5$$

Multiply 3 and 2 to get 6.

$$4x^{3}-5x^{2}+9x+25+6x^{3}-3x^{2}+5x-5$$

Combine 4x^{3} and 6x^{3} to get 10x^{3}.

$$10x^{3}-5x^{2}+9x+25-3x^{2}+5x-5$$

Combine -5x^{2} and -3x^{2} to get -8x^{2}.

$$10x^{3}-8x^{2}+9x+25+5x-5$$

Combine 9x and 5x to get 14x.

$$10x^{3}-8x^{2}+14x+25-5$$

Subtract 5 from 25 to get 20.

$$10x^{3}-8x^{2}+14x+20$$

Factor

$$2\left(5x^{3}-4x^{2}+7x+10\right)$$

Solution Steps

Multiply and combine like terms.

$$10x^{3}-8x^{2}+14x+20$$

Factor out 2. Polynomial 5x^{3}-4x^{2}+7x+10 is not factored since it does not have any rational roots.

$$2\left(5x^{3}-4x^{2}+7x+10\right)$$