Solve 2x^4-3x^3-11x^2 12x 9

Question

Simplify the expression

2 x^{4} - 1191 x^{3}

Evaluate

2 x^{4} - 3 x^{3} - 11 x^{2} \times 12 x \times 9

Multiply

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Multiply the terms

- 11 x^{2} \times 12 x \times 9

Multiply the terms

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Evaluate

11 \times 12 \times 9

Multiply the terms

132 \times 9

Multiply the numbers

1188

- 1188 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 1188 x^{2 + 1}

Add the numbers

- 1188 x^{3}

2 x^{4} - 3 x^{3} - 1188 x^{3}

Solution

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Evaluate

- 3 x^{3} - 1188 x^{3}

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

(- 3 - 1188) x^{3}

Subtract the numbers

- 1191 x^{3}

2 x^{4} - 1191 x^{3}

Show Solution

Factor the expression

x^{3} (2 x - 1191)

Evaluate

2 x^{4} - 3 x^{3} - 11 x^{2} \times 12 x \times 9

Multiply

More Steps

Multiply the terms

11 x^{2} \times 12 x \times 9

Multiply the terms

More Steps

Evaluate

11 \times 12 \times 9

Multiply the terms

132 \times 9

Multiply the numbers

1188

1188 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1188 x^{2 + 1}

Add the numbers

1188 x^{3}

2 x^{4} - 3 x^{3} - 1188 x^{3}

Subtract the terms

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Evaluate

- 3 x^{3} - 1188 x^{3}

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

(- 3 - 1188) x^{3}

Subtract the numbers

- 1191 x^{3}

2 x^{4} - 1191 x^{3}

Rewrite the expression

x^{3} \times 2 x - x^{3} \times 1191

Solution

x^{3} (2 x - 1191)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{1191}{2}

Alternative Form

x_{1} = 0, x_{2} = 595.5

Evaluate

2 x^{4} - 3 x^{3} - 11 x^{2} \times 12 x \times 9

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

2 x^{4} - 3 x^{3} - 11 x^{2} \times 12 x \times 9 = 0

Multiply

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Multiply the terms

11 x^{2} \times 12 x \times 9

Multiply the terms

More Steps

Evaluate

11 \times 12 \times 9

Multiply the terms

132 \times 9

Multiply the numbers

1188

1188 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1188 x^{2 + 1}

Add the numbers

1188 x^{3}

2 x^{4} - 3 x^{3} - 1188 x^{3} = 0

Subtract the terms

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Simplify

2 x^{4} - 3 x^{3} - 1188 x^{3}

Subtract the terms

More Steps

Evaluate

- 3 x^{3} - 1188 x^{3}

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

(- 3 - 1188) x^{3}

Subtract the numbers

- 1191 x^{3}

2 x^{4} - 1191 x^{3}

2 x^{4} - 1191 x^{3} = 0

Factor the expression

x^{3} (2 x - 1191) = 0

Separate the equation into 2 possible cases

x^{3} = 0 2 x - 1191 = 0

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

x = 0 2 x - 1191 = 0

Solve the equation

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Evaluate

2 x - 1191 = 0

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

2 x = 0 + 1191

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

2 x = 1191

Divide both sides

\frac{2 x}{2} = \frac{1191}{2}

Divide the numbers

x = \frac{1191}{2}

x = 0 x = \frac{1191}{2}

Solution

x_{1} = 0, x_{2} = \frac{1191}{2}

Alternative Form

x_{1} = 0, x_{2} = 595.5

Show Solution