Solve 8x^2-32x

$$8 x ^ { 2 } - 32 x$$

Factor

$$8x\left(x-4\right)$$

Solution Steps

Factor out 8.

$$8\left(x^{2}-4x\right)$$

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

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

Rewrite the complete factored expression.

$$8x\left(x-4\right)$$

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.

$$8x^{2}-32x=0$$

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.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}}}{2\times 8}$$

Take the square root of \left(-32\right)^{2}.

$$x=\frac{-\left(-32\right)±32}{2\times 8}$$

The opposite of -32 is 32.

$$x=\frac{32±32}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{32±32}{16}$$

Now solve the equation x=\frac{32±32}{16} when ± is plus. Add 32 to 32.

$$x=\frac{64}{16}$$

Divide 64 by 16.

$$x=4$$

Now solve the equation x=\frac{32±32}{16} when ± is minus. Subtract 32 from 32.

$$x=\frac{0}{16}$$

Divide 0 by 16.

$$x=0$$

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}.

$$8x^{2}-32x=8\left(x-4\right)x$$

Evaluate

$$8x\left(x-4\right)$$