Solve 3x^(4)-2x^(3)-4x^(2)-4x 12 / x^(2) 2x^2

Question

Simplify the expression

3 x^{4} - 2 x^{3} - 4 x^{2} - 96 x

Evaluate

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

Solution

More Steps

Evaluate

- 4 x \times \frac{12}{x ^{2}} \times 2 x^{2}

Multiply the terms

- 8 x \times \frac{12}{x ^{2}} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 8 x^{1 + 2} \times \frac{12}{x ^{2}}

Add the numbers

- 8 x^{3} \times \frac{12}{x ^{2}}

Multiply the terms

More Steps

Multiply the terms

8 x^{3} \times \frac{12}{x ^{2}}

Cancel out the common factor x^{2}

8 x \times 12

Multiply the terms

96 x

- 96 x

3 x^{4} - 2 x^{3} - 4 x^{2} - 96 x

Show Solution

x = 0

Evaluate

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

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

x^{2} = 0

Solution

x = 0

Show Solution

x (3 x^{3} - 2 x^{2} - 4 x - 96)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

8 x \times \frac{12}{x ^{2}} \times x^{2}

Multiply the terms with the same base by adding their exponents

8 x^{1 + 2} \times \frac{12}{x ^{2}}

Add the numbers

8 x^{3} \times \frac{12}{x ^{2}}

Cancel out the common factor x^{2}

8 x \times 12

Multiply the terms

96 x

3 x^{4} - 2 x^{3} - 4 x^{2} - 96 x

Rewrite the expression

x \times 3 x^{3} - x \times 2 x^{2} - x \times 4 x - x \times 96

Solution

x (3 x^{3} - 2 x^{2} - 4 x - 96)

Show Solution

x \approx 3.562431

Evaluate

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

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

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

The only way a power can not be 0 is when the base not equals 0

3 x^{4} - 2 x^{3} - 4 x^{2} - 4 x \times \frac{12}{x ^{2}} \times 2 x^{2} = 0, x \neq = 0

Calculate

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

8 x \times \frac{12}{x ^{2}} \times x^{2}

Multiply the terms with the same base by adding their exponents

8 x^{1 + 2} \times \frac{12}{x ^{2}}

Add the numbers

8 x^{3} \times \frac{12}{x ^{2}}

Cancel out the common factor x^{2}

8 x \times 12

Multiply the terms

96 x

3 x^{4} - 2 x^{3} - 4 x^{2} - 96 x = 0

Factor the expression

x (3 x^{3} - 2 x^{2} - 4 x - 96) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{3} - 2 x^{2} - 4 x - 96 = 0

Solve the equation

x = 0 x \approx 3.562431

Check if the solution is in the defined range

x = 0 x \approx 3.562431, x \neq = 0

Solution

x \approx 3.562431

Show Solution