Solve (s-2)(s^2)(s-3)

Question

Simplify the expression

s^{4} - 5 s^{3} + 6 s^{2}

Evaluate

(s - 2) s^{2} (s - 3)

Multiply the first two terms

s^{2} (s - 2) (s - 3)

Multiply the terms

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Evaluate

s^{2} (s - 2)

Apply the distributive property

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

Multiply the terms

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Evaluate

s^{2} \times s

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

s^{2 + 1}

Add the numbers

s^{3}

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

Use the commutative property to reorder the terms

s^{3} - 2 s^{2}

(s^{3} - 2 s^{2}) (s - 3)

Apply the distributive property

s^{3} \times s - s^{3} \times 3 - 2 s^{2} \times s - (- 2 s^{2} \times 3)

Multiply the terms

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Evaluate

s^{3} \times s

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

s^{3 + 1}

Add the numbers

s^{4}

s^{4} - s^{3} \times 3 - 2 s^{2} \times s - (- 2 s^{2} \times 3)

Use the commutative property to reorder the terms

s^{4} - 3 s^{3} - 2 s^{2} \times s - (- 2 s^{2} \times 3)

Multiply the terms

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Evaluate

s^{2} \times s

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

s^{2 + 1}

Add the numbers

s^{3}

s^{4} - 3 s^{3} - 2 s^{3} - (- 2 s^{2} \times 3)

Multiply the numbers

s^{4} - 3 s^{3} - 2 s^{3} - (- 6 s^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

s^{4} - 3 s^{3} - 2 s^{3} + 6 s^{2}

Solution

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Evaluate

- 3 s^{3} - 2 s^{3}

Collect like terms by calculating the sum or difference of their coefficients

(- 3 - 2) s^{3}

Subtract the numbers

- 5 s^{3}

s^{4} - 5 s^{3} + 6 s^{2}

Show Solution

Find the roots

s_{1} = 0, s_{2} = 2, s_{3} = 3

Evaluate

(s - 2) (s^{2}) (s - 3)

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

(s - 2) (s^{2}) (s - 3) = 0

Calculate

(s - 2) s^{2} (s - 3) = 0

Multiply the first two terms

s^{2} (s - 2) (s - 3) = 0

Separate the equation into 3 possible cases

s^{2} = 0 s - 2 = 0 s - 3 = 0

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

s = 0 s - 2 = 0 s - 3 = 0

Solve the equation

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Evaluate

s - 2 = 0

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

s = 0 + 2

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

s = 2

s = 0 s = 2 s - 3 = 0

Solve the equation

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Evaluate

s - 3 = 0

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

s = 0 + 3

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

s = 3

s = 0 s = 2 s = 3

Solution

s_{1} = 0, s_{2} = 2, s_{3} = 3

Show Solution