Solve 4x+2x^2+12

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

Factor

$$2\left(x^{2}+2x+6\right)$$

Solution Steps

Factor out 2. Polynomial 2x+x^{2}+6 is not factored since it does not have any rational roots.

$$2\left(2x+x^{2}+6\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$2x^{2}+4x+12=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-4±\sqrt{4^{2}-4\times 2\times 12}}{2\times 2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 2\times 12}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-4±\sqrt{16-8\times 12}}{2\times 2}$$

Multiply -8 times 12.

$$x=\frac{-4±\sqrt{16-96}}{2\times 2}$$

Add 16 to -96.

$$x=\frac{-4±\sqrt{-80}}{2\times 2}$$

Since the square root of a negative number is not defined in the real field, there are no solutions. Quadratic polynomial cannot be factored.

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

Evaluate

$$2\left(x^{2}+2x+6\right)$$