Solve (12x^2+4x+4)

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

Factor

$$4\left(3x^{2}+x+1\right)$$

Solution Steps

Factor out 4. Polynomial 3x^{2}+x+1 is not factored since it does not have any rational roots.

$$4\left(3x^{2}+x+1\right)$$

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.

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

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.

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

Square 4.

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

Multiply -4 times 12.

$$x=\frac{-4±\sqrt{16-48\times 4}}{2\times 12}$$

Multiply -48 times 4.

$$x=\frac{-4±\sqrt{16-192}}{2\times 12}$$

Add 16 to -192.

$$x=\frac{-4±\sqrt{-176}}{2\times 12}$$

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

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

Evaluate

$$4\left(3x^{2}+x+1\right)$$