Solve lambda^2-24lambda

$$\lambda ^ { 2 } - 24 \lambda$$

Factor

$$\lambda \left(\lambda -24\right)$$

Solution Steps

Factor out \lambda .

$$\lambda \left(\lambda -24\right)$$

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.

$$\lambda ^{2}-24\lambda =0$$

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.

$$\lambda =\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2}$$

Take the square root of \left(-24\right)^{2}.

$$\lambda =\frac{-\left(-24\right)±24}{2}$$

The opposite of -24 is 24.

$$\lambda =\frac{24±24}{2}$$

Now solve the equation \lambda =\frac{24±24}{2} when ± is plus. Add 24 to 24.

$$\lambda =\frac{48}{2}$$

Divide 48 by 2.

$$\lambda =24$$

Now solve the equation \lambda =\frac{24±24}{2} when ± is minus. Subtract 24 from 24.

$$\lambda =\frac{0}{2}$$

Divide 0 by 2.

$$\lambda =0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 24 for x_{1} and 0 for x_{2}.

$$\lambda ^{2}-24\lambda =\left(\lambda -24\right)\lambda$$

Evaluate

$$\lambda \left(\lambda -24\right)$$