Solve 2a^3+5a^2-4a+6a^2+15a-12=

$$2 a ^ { 3 } + 5 a ^ { 2 } - 4 a + 6 a ^ { 2 } + 15 a - 12 =$$

Evaluate

$$\left(a+3\right)\left(2a^{2}+5a-4\right)$$

Solution Steps

Combine 5a^{2} and 6a^{2} to get 11a^{2}.

$$2a^{3}+11a^{2}-4a+15a-12$$

Combine -4a and 15a to get 11a.

$$2a^{3}+11a^{2}+11a-12$$

Factor

$$2\left(a+3\right)\left(a-\frac{-\sqrt{57}-5}{4}\right)\left(a-\frac{\sqrt{57}-5}{4}\right)$$

Solution Steps

Multiply and combine like terms.

$$2a^{3}+11a^{2}+11a-12$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -12 and q divides the leading coefficient 2. One such root is -3. Factor the polynomial by dividing it by a+3. Polynomial 2a^{2}+5a-4 is not factored since it does not have any rational roots.

$$\left(a+3\right)\left(2a^{2}+5a-4\right)$$