Solve 4x^2+8x+12+x^3+2x^2+3x

$$4 { x }^{ 2 } +8x+12+ { x }^{ 3 } +2 { x }^{ 2 } +3x$$

Evaluate

$$\left(x+4\right)\left(x^{2}+2x+3\right)$$

Solution Steps

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+8x+12+x^{3}+3x$$

Combine 8x and 3x to get 11x.

$$6x^{2}+11x+12+x^{3}$$

Factor

$$\left(x+4\right)\left(x^{2}+2x+3\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{3}+6x^{2}+11x+12$$

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 1. One such root is -4. Factor the polynomial by dividing it by x+4. Polynomial x^{2}+2x+3 is not factored since it does not have any rational roots.

$$\left(x+4\right)\left(x^{2}+2x+3\right)$$