Solve (2x^34x^2 - 32x 18) / (x - 3)

Question

Simplify the expression

\frac{8 x ^{5} - 576 x}{x - 3}

Evaluate

\frac{2 x ^{3} \times 4 x ^{2} - 32 x \times 18}{x - 3}

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

8 x^{3 + 2}

Add the numbers

8 x^{5}

\frac{8 x ^{5} - 32 x \times 18}{x - 3}

Solution

\frac{8 x ^{5} - 576 x}{x - 3}

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Find the excluded values

x = 3

Evaluate

\frac{2 x ^{3} \times 4 x ^{2} - 32 x \times 18}{x - 3}

To find the excluded values,set the denominators equal to 0

x - 3 = 0

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

x = 0 + 3

Solution

x = 3

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Find the roots

x_{1} = - 472, x_{2} = 0, x_{3} = 472

Alternative Form

x_{1} \approx - 2.912951, x_{2} = 0, x_{3} \approx 2.912951

Evaluate

\frac{2 x ^{3} \times 4 x ^{2} - 32 x \times 18}{x - 3}

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

\frac{2 x ^{3} \times 4 x ^{2} - 32 x \times 18}{x - 3} = 0

Find the domain

More Steps

Evaluate

x - 3 \neq = 0

Move the constant to the right side

x \neq = 0 + 3

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

x \neq = 3

\frac{2 x ^{3} \times 4 x ^{2} - 32 x \times 18}{x - 3} = 0, x \neq = 3

Calculate

\frac{2 x ^{3} \times 4 x ^{2} - 32 x \times 18}{x - 3} = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

8 x^{3 + 2}

Add the numbers

8 x^{5}

\frac{8 x ^{5} - 32 x \times 18}{x - 3} = 0

Multiply the terms

\frac{8 x ^{5} - 576 x}{x - 3} = 0

Cross multiply

8 x^{5} - 576 x = (x - 3) \times 0

Simplify the equation

8 x^{5} - 576 x = 0

Factor the expression

8 x (x^{4} - 72) = 0

Divide both sides

x (x^{4} - 72) = 0

Separate the equation into 2 possible cases

x = 0 x^{4} - 72 = 0

Solve the equation

More Steps

Evaluate

x^{4} - 72 = 0

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

x^{4} = 0 + 72

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

x^{4} = 72

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

x = \pm 472

Separate the equation into 2 possible cases

x = 472 x = - 472

x = 0 x = 472 x = - 472

Check if the solution is in the defined range

x = 0 x = 472 x = - 472, x \neq = 3

Find the intersection of the solution and the defined range

x = 0 x = 472 x = - 472

Solution

x_{1} = - 472, x_{2} = 0, x_{3} = 472

Alternative Form

x_{1} \approx - 2.912951, x_{2} = 0, x_{3} \approx 2.912951

Show Solution