Solve (2a^{4}-2a^{3}+3a^{2}-a+7)+(2a^2-3a^3+a-6)+(2a^3-2a^2-5)

$$( 2 a ^ { 4 } - 2 a ^ { 3 } + 3 a ^ { 2 } - a + 7 ) + ( 2 a ^ { 2 } - 3 a ^ { 3 } + a - 6 ) + ( 2 a ^ { 3 } - 2 a ^ { 2 } - 5 )$$

Evaluate

$$2a^{4}-3a^{3}+3a^{2}-4$$

Solution Steps

Combine 3a^{2} and 2a^{2} to get 5a^{2}.

$$2a^{4}-2a^{3}+5a^{2}-a+7-3a^{3}+a-6+2a^{3}-2a^{2}-5$$

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

$$2a^{4}-5a^{3}+5a^{2}-a+7+a-6+2a^{3}-2a^{2}-5$$

Combine -a and a to get 0.

$$2a^{4}-5a^{3}+5a^{2}+7-6+2a^{3}-2a^{2}-5$$

Subtract 6 from 7 to get 1.

$$2a^{4}-5a^{3}+5a^{2}+1+2a^{3}-2a^{2}-5$$

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

$$2a^{4}-3a^{3}+5a^{2}+1-2a^{2}-5$$

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

$$2a^{4}-3a^{3}+3a^{2}+1-5$$

Subtract 5 from 1 to get -4.

$$2a^{4}-3a^{3}+3a^{2}-4$$

Factor

$$2\left(a-\frac{1-\sqrt{17}}{4}\right)\left(a-\frac{\sqrt{17}+1}{4}\right)\left(a^{2}-a+2\right)$$