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k\left(k-8\right)
Factor out k.
k^{2}-8k=0
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.
k=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2}
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.
k=\frac{-\left(-8\right)±8}{2}
Take the square root of \left(-8\right)^{2}.
k=\frac{8±8}{2}
The opposite of -8 is 8.
k=\frac{16}{2}
Now solve the equation k=\frac{8±8}{2} when ± is plus. Add 8 to 8.
k=8
Divide 16 by 2.
k=\frac{0}{2}
Now solve the equation k=\frac{8±8}{2} when ± is minus. Subtract 8 from 8.
k=0
Divide 0 by 2.
k^{2}-8k=\left(k-8\right)k
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 8 for x_{1} and 0 for x_{2}.