Solve 4x^3 12x^2-40x

Question

Simplify the expression

48 x^{5} - 40 x

Evaluate

4 x^{3} \times 12 x^{2} - 40 x

Solution

More Steps

Evaluate

4 x^{3} \times 12 x^{2}

Multiply the terms

48 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

48 x^{3 + 2}

Add the numbers

48 x^{5}

48 x^{5} - 40 x

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Factor the expression

8 x (6 x^{4} - 5)

Evaluate

4 x^{3} \times 12 x^{2} - 40 x

Multiply

More Steps

Evaluate

4 x^{3} \times 12 x^{2}

Multiply the terms

48 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

48 x^{3 + 2}

Add the numbers

48 x^{5}

48 x^{5} - 40 x

Rewrite the expression

8 x \times 6 x^{4} - 8 x \times 5

Solution

8 x (6 x^{4} - 5)

Show Solution

Find the roots

x_{1} = - \frac{4 1080}{6}, x_{2} = 0, x_{3} = \frac{4 1080}{6}

Alternative Form

x_{1} \approx - 0.955443, x_{2} = 0, x_{3} \approx 0.955443

Evaluate

4 x^{3} \times 12 x^{2} - 40 x

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

4 x^{3} \times 12 x^{2} - 40 x = 0

Multiply

More Steps

Multiply the terms

4 x^{3} \times 12 x^{2}

Multiply the terms

48 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

48 x^{3 + 2}

Add the numbers

48 x^{5}

48 x^{5} - 40 x = 0

Factor the expression

8 x (6 x^{4} - 5) = 0

Divide both sides

x (6 x^{4} - 5) = 0

Separate the equation into 2 possible cases

x = 0 6 x^{4} - 5 = 0

Solve the equation

More Steps

Evaluate

6 x^{4} - 5 = 0

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

6 x^{4} = 0 + 5

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

6 x^{4} = 5

Divide both sides

\frac{6 x ^{4}}{6} = \frac{5}{6}

Divide the numbers

x^{4} = \frac{5}{6}

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

x = \pm 4 \frac{5}{6}

Simplify the expression

More Steps

Evaluate

4 \frac{5}{6}

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

\frac{4 5}{4 6}

Multiply by the Conjugate

\frac{4 5 \times 4 6 ^{3}}{4 6 \times 4 6 ^{3}}

Simplify

\frac{4 5 \times 4 216}{4 6 \times 4 6 ^{3}}

Multiply the numbers

\frac{4 1080}{4 6 \times 4 6 ^{3}}

Multiply the numbers

\frac{4 1080}{6}

x = \pm \frac{4 1080}{6}

Separate the equation into 2 possible cases

x = \frac{4 1080}{6} x = - \frac{4 1080}{6}

x = 0 x = \frac{4 1080}{6} x = - \frac{4 1080}{6}

Solution

x_{1} = - \frac{4 1080}{6}, x_{2} = 0, x_{3} = \frac{4 1080}{6}

Alternative Form

x_{1} \approx - 0.955443, x_{2} = 0, x_{3} \approx 0.955443

Show Solution