Solve (-5a^3+8a^2+4)+(2a^3-4a^2+2a)

$$( - 5 a ^ { 3 } + 8 a ^ { 2 } + 4 ) + ( 2 a ^ { 3 } - 4 a ^ { 2 } + 2 a )$$

Evaluate

$$-\left(a-2\right)\left(3a^{2}+2a+2\right)$$

Solution Steps

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

$$-3a^{3}+8a^{2}+4-4a^{2}+2a$$

Combine 8a^{2} and -4a^{2} to get 4a^{2}.

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

Factor

$$-\left(a-2\right)\left(3a^{2}+2a+2\right)$$

Solution Steps

Multiply and combine like terms.

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

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 4 and q divides the leading coefficient -3. One such root is 2. Factor the polynomial by dividing it by a-2. Polynomial -3a^{2}-2a-2 is not factored since it does not have any rational roots.

$$\left(a-2\right)\left(-3a^{2}-2a-2\right)$$