Solve (k^3 - 13k^235k^33) / (k - 8)

Question

Simplify the expression

\frac{k ^{3} - 1365 k ^{5}}{k - 8}

Show Solution

k = 8

Show Solution

k_{1} = - \frac{1365}{1365}, k_{2} = 0, k_{3} = \frac{1365}{1365}

Alternative Form

k_{1} \approx - 0.027067, k_{2} = 0, k_{3} \approx 0.027067

Evaluate

(k^{3} - 13 k^{2} \times 35 k^{3} \times 3) \div (k - 8)

To find the roots of the expression,set the expression equal to 0

(k^{3} - 13 k^{2} \times 35 k^{3} \times 3) \div (k - 8) = 0

Find the domain

More Steps

(k^{3} - 13 k^{2} \times 35 k^{3} \times 3) \div (k - 8) = 0, k \neq = 8

Calculate

(k^{3} - 13 k^{2} \times 35 k^{3} \times 3) \div (k - 8) = 0

Multiply

More Steps

(k^{3} - 1365 k^{5}) \div (k - 8) = 0

Rewrite the expression

\frac{k ^{3} - 1365 k ^{5}}{k - 8} = 0

Cross multiply

k^{3} - 1365 k^{5} = (k - 8) \times 0

Simplify the equation

k^{3} - 1365 k^{5} = 0

Factor the expression

k^{3} (1 - 1365 k^{2}) = 0

Separate the equation into 2 possible cases

k^{3} = 0 1 - 1365 k^{2} = 0

The only way a power can be 0 is when the base equals 0

k = 0 1 - 1365 k^{2} = 0

Solve the equation

More Steps

k = 0 k = \frac{1365}{1365} k = - \frac{1365}{1365}

Check if the solution is in the defined range

k = 0 k = \frac{1365}{1365} k = - \frac{1365}{1365}, k \neq = 8

Find the intersection of the solution and the defined range

k = 0 k = \frac{1365}{1365} k = - \frac{1365}{1365}

Solution

k_{1} = - \frac{1365}{1365}, k_{2} = 0, k_{3} = \frac{1365}{1365}

Alternative Form

k_{1} \approx - 0.027067, k_{2} = 0, k_{3} \approx 0.027067

Show Solution