Solve (x^6)(-4x^(3)-x^(2) 4x-2)

Question

Simplify the expression

- 8 x^{9} - 2 x^{6}

Evaluate

x^{6} (- 4 x^{3} - x^{2} \times 4 x - 2)

Multiply

More Steps

Multiply the terms

- x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 4

Add the numbers

- x^{3} \times 4

Use the commutative property to reorder the terms

- 4 x^{3}

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

Subtract the terms

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Evaluate

- 4 x^{3} - 4 x^{3} - 2

Subtract the terms

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Evaluate

- 4 x^{3} - 4 x^{3}

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

(- 4 - 4) x^{3}

Subtract the numbers

- 8 x^{3}

- 8 x^{3} - 2

x^{6} (- 8 x^{3} - 2)

Apply the distributive property

x^{6} (- 8 x^{3}) - x^{6} \times 2

Multiply the terms

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Evaluate

x^{6} (- 8 x^{3})

Use the commutative property to reorder the terms

- 8 x^{6} \times x^{3}

Multiply the terms

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Evaluate

x^{6} \times x^{3}

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

x^{6 + 3}

Add the numbers

x^{9}

- 8 x^{9}

- 8 x^{9} - x^{6} \times 2

Solution

- 8 x^{9} - 2 x^{6}

Show Solution

Factor the expression

- 2 x^{6} (4 x^{3} + 1)

Evaluate

x^{6} (- 4 x^{3} - x^{2} \times 4 x - 2)

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

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

Subtract the terms

More Steps

Simplify

- 4 x^{3} - 4 x^{3}

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

(- 4 - 4) x^{3}

Subtract the numbers

- 8 x^{3}

x^{6} (- 8 x^{3} - 2)

Factor the expression

x^{6} (- 2) (4 x^{3} + 1)

Solution

- 2 x^{6} (4 x^{3} + 1)

Show Solution

Find the roots

x_{1} = - \frac{3 2}{2}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.629961, x_{2} = 0

Evaluate

(x^{6}) (- 4 x^{3} - x^{2} \times 4 x - 2)

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

(x^{6}) (- 4 x^{3} - x^{2} \times 4 x - 2) = 0

Calculate

x^{6} (- 4 x^{3} - x^{2} \times 4 x - 2) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

x^{6} (- 4 x^{3} - 4 x^{3} - 2) = 0

Subtract the terms

More Steps

Simplify

- 4 x^{3} - 4 x^{3}

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

(- 4 - 4) x^{3}

Subtract the numbers

- 8 x^{3}

x^{6} (- 8 x^{3} - 2) = 0

Separate the equation into 2 possible cases

x^{6} = 0 - 8 x^{3} - 2 = 0

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

x = 0 - 8 x^{3} - 2 = 0

Solve the equation

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Evaluate

- 8 x^{3} - 2 = 0

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

- 8 x^{3} = 0 + 2

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

- 8 x^{3} = 2

Change the signs on both sides of the equation

8 x^{3} = - 2

Divide both sides

\frac{8 x ^{3}}{8} = \frac{- 2}{8}

Divide the numbers

x^{3} = \frac{- 2}{8}

Divide the numbers

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Evaluate

\frac{- 2}{8}

Cancel out the common factor 2

\frac{- 1}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{4}

x^{3} = - \frac{1}{4}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{1}{4}

Calculate

x = 3 - \frac{1}{4}

Simplify the root

More Steps

Evaluate

3 - \frac{1}{4}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{4}

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

- \frac{3 1}{3 4}

Simplify the radical expression

- \frac{1}{3 4}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

\frac{- 2 3 2}{2 ^{2}}

Reduce the fraction

\frac{- 3 2}{2}

Calculate

- \frac{3 2}{2}

x = - \frac{3 2}{2}

x = 0 x = - \frac{3 2}{2}

Solution

x_{1} = - \frac{3 2}{2}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.629961, x_{2} = 0

Show Solution