Solve 4x^2-16x

$$4 { x }^{ 2 } -16x$$

Factor

$$4x\left(x-4\right)$$

Solution Steps

Factor out 4.

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

Consider x^{2}-4x. Factor out x.

$$x\left(x-4\right)$$

Rewrite the complete factored expression.

$$4x\left(x-4\right)$$

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.

$$4x^{2}-16x=0$$

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.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}}}{2\times 4}$$

Take the square root of \left(-16\right)^{2}.

$$x=\frac{-\left(-16\right)±16}{2\times 4}$$

The opposite of -16 is 16.

$$x=\frac{16±16}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{16±16}{8}$$

Now solve the equation x=\frac{16±16}{8} when ± is plus. Add 16 to 16.

$$x=\frac{32}{8}$$

Divide 32 by 8.

$$x=4$$

Now solve the equation x=\frac{16±16}{8} when ± is minus. Subtract 16 from 16.

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

Divide 0 by 8.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 4 for x_{1} and 0 for x_{2}.

$$4x^{2}-16x=4\left(x-4\right)x$$

Evaluate

$$4x\left(x-4\right)$$