Solve 3/2 p^4(-2p- 5/2 )

Question

Simplify the expression

- 3 p^{5} - \frac{15}{4} p^{4}

Evaluate

\frac{3}{2} p^{4} (- 2 p - \frac{5}{2})

Apply the distributive property

\frac{3}{2} p^{4} (- 2 p) - \frac{3}{2} p^{4} \times \frac{5}{2}

Multiply the terms

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Evaluate

\frac{3}{2} p^{4} (- 2 p)

Multiply the numbers

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Evaluate

\frac{3}{2} (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- \frac{3}{2} \times 2

Reduce the numbers

- 3 \times 1

Simplify

- 3

- 3 p^{4} \times p

Multiply the terms

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Evaluate

p^{4} \times p

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

p^{4 + 1}

Add the numbers

p^{5}

- 3 p^{5}

- 3 p^{5} - \frac{3}{2} p^{4} \times \frac{5}{2}

Solution

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Evaluate

\frac{3}{2} \times \frac{5}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3 \times 5}{2 \times 2}

Multiply the numbers

\frac{15}{2 \times 2}

Multiply the numbers

\frac{15}{4}

- 3 p^{5} - \frac{15}{4} p^{4}

Show Solution

Factor the expression

- \frac{3}{4} p^{4} (4 p + 5)

Evaluate

\frac{3}{2} p^{4} (- 2 p - \frac{5}{2})

Factor the expression

\frac{3}{2} p^{4} (- \frac{1}{2}) (4 p + 5)

Solution

- \frac{3}{4} p^{4} (4 p + 5)

Show Solution

Find the roots

p_{1} = - \frac{5}{4}, p_{2} = 0

Alternative Form

p_{1} = - 1.25, p_{2} = 0

Evaluate

\frac{3}{2} p^{4} (- 2 p - \frac{5}{2})

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

\frac{3}{2} p^{4} (- 2 p - \frac{5}{2}) = 0

Elimination the left coefficient

p^{4} (- 2 p - \frac{5}{2}) = 0

Separate the equation into 2 possible cases

p^{4} = 0 - 2 p - \frac{5}{2} = 0

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

p = 0 - 2 p - \frac{5}{2} = 0

Solve the equation

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Evaluate

- 2 p - \frac{5}{2} = 0

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

- 2 p = 0 + \frac{5}{2}

Add the terms

- 2 p = \frac{5}{2}

Change the signs on both sides of the equation

2 p = - \frac{5}{2}

Multiply by the reciprocal

2 p \times \frac{1}{2} = - \frac{5}{2} \times \frac{1}{2}

Multiply

p = - \frac{5}{2} \times \frac{1}{2}

Multiply

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Evaluate

- \frac{5}{2} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{5}{2 \times 2}

Multiply the numbers

- \frac{5}{4}

p = - \frac{5}{4}

p = 0 p = - \frac{5}{4}

Solution

p_{1} = - \frac{5}{4}, p_{2} = 0

Alternative Form

p_{1} = - 1.25, p_{2} = 0

Show Solution