Solve 2x+6x^2+2

$$2 x + 6 x ^ { 2 } + 2$$

Factor

$$2\left(3x^{2}+x+1\right)$$

Solution Steps

Factor out 2. Polynomial x+3x^{2}+1 is not factored since it does not have any rational roots.

$$2\left(x+3x^{2}+1\right)$$

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.

$$6x^{2}+2x+2=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\times 6\times 2}}{2\times 6}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\times 6\times 2}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{-2±\sqrt{4-24\times 2}}{2\times 6}$$

Multiply -24 times 2.

$$x=\frac{-2±\sqrt{4-48}}{2\times 6}$$

Add 4 to -48.

$$x=\frac{-2±\sqrt{-44}}{2\times 6}$$

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

$$6x^{2}+2x+2$$

Evaluate

$$2\left(3x^{2}+x+1\right)$$