Solve f(x)=-4x^2-16x

$$f ( x ) = - 4 x ^ { 2 } - 16 x$$

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.

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

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

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

The opposite of -16 is 16.

$$x=\frac{16±16}{2\left(-4\right)}$$

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}.

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

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

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

Evaluate

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