Solve 4x^2+2x

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

Factor

$$2x\left(2x+1\right)$$

Solution Steps

Factor out 2.

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

Consider 2x^{2}+x. Factor out x.

$$x\left(2x+1\right)$$

Rewrite the complete factored expression.

$$2x\left(2x+1\right)$$

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.

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

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.

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

Take the square root of 2^{2}.

$$x=\frac{-2±2}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-2±2}{8}$$

Now solve the equation x=\frac{-2±2}{8} when ± is plus. Add -2 to 2.

$$x=\frac{0}{8}$$

Divide 0 by 8.

$$x=0$$

Now solve the equation x=\frac{-2±2}{8} when ± is minus. Subtract 2 from -2.

$$x=-\frac{4}{8}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -\frac{1}{2} for x_{2}.

$$4x^{2}+2x=4x\left(x-\left(-\frac{1}{2}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

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

Add \frac{1}{2} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$4x^{2}+2x=4x\times \frac{2x+1}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

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

Evaluate

$$2x\left(2x+1\right)$$