Solve s^33s^2 -40s

Question

Simplify the expression

3 s^{5} - 40 s

Evaluate

s^{3} \times 3 s^{2} - 40 s

Solution

More Steps

Evaluate

s^{3} \times 3 s^{2}

Multiply the terms with the same base by adding their exponents

s^{3 + 2} \times 3

Add the numbers

s^{5} \times 3

Use the commutative property to reorder the terms

3 s^{5}

3 s^{5} - 40 s

Show Solution

Factor the expression

s (3 s^{4} - 40)

Evaluate

s^{3} \times 3 s^{2} - 40 s

Multiply

More Steps

Evaluate

s^{3} \times 3 s^{2}

Multiply the terms with the same base by adding their exponents

s^{3 + 2} \times 3

Add the numbers

s^{5} \times 3

Use the commutative property to reorder the terms

3 s^{5}

3 s^{5} - 40 s

Rewrite the expression

s \times 3 s^{4} - s \times 40

Solution

s (3 s^{4} - 40)

Show Solution

Find the roots

s_{1} = - \frac{4 1080}{3}, s_{2} = 0, s_{3} = \frac{4 1080}{3}

Alternative Form

s_{1} \approx - 1.910886, s_{2} = 0, s_{3} \approx 1.910886

Evaluate

s^{3} \times 3 s^{2} - 40 s

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

s^{3} \times 3 s^{2} - 40 s = 0

Multiply

More Steps

Multiply the terms

s^{3} \times 3 s^{2}

Multiply the terms with the same base by adding their exponents

s^{3 + 2} \times 3

Add the numbers

s^{5} \times 3

Use the commutative property to reorder the terms

3 s^{5}

3 s^{5} - 40 s = 0

Factor the expression

s (3 s^{4} - 40) = 0

Separate the equation into 2 possible cases

s = 0 3 s^{4} - 40 = 0

Solve the equation

More Steps

Evaluate

3 s^{4} - 40 = 0

Move the constant to the right-hand side and change its sign

3 s^{4} = 0 + 40

Removing 0 doesn't change the value,so remove it from the expression

3 s^{4} = 40

Divide both sides

\frac{3 s ^{4}}{3} = \frac{40}{3}

Divide the numbers

s^{4} = \frac{40}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

s = \pm 4 \frac{40}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{40}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 40}{4 3}

Multiply by the Conjugate

\frac{4 40 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 40 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 1080}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 1080}{3}

s = \pm \frac{4 1080}{3}

Separate the equation into 2 possible cases

s = \frac{4 1080}{3} s = - \frac{4 1080}{3}

s = 0 s = \frac{4 1080}{3} s = - \frac{4 1080}{3}

Solution

s_{1} = - \frac{4 1080}{3}, s_{2} = 0, s_{3} = \frac{4 1080}{3}

Alternative Form

s_{1} \approx - 1.910886, s_{2} = 0, s_{3} \approx 1.910886

Show Solution