Solve x^4-2x^3-7x^2 8x 12

Question

Simplify the expression

x^{4} - 674 x^{3}

Evaluate

x^{4} - 2 x^{3} - 7 x^{2} \times 8 x \times 12

Multiply

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Multiply the terms

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

Multiply the terms

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Evaluate

7 \times 8 \times 12

Multiply the terms

56 \times 12

Multiply the numbers

672

- 672 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 672 x^{2 + 1}

Add the numbers

- 672 x^{3}

x^{4} - 2 x^{3} - 672 x^{3}

Solution

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Evaluate

- 2 x^{3} - 672 x^{3}

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

(- 2 - 672) x^{3}

Subtract the numbers

- 674 x^{3}

x^{4} - 674 x^{3}

Show Solution

Factor the expression

x^{3} (x - 674)

Evaluate

x^{4} - 2 x^{3} - 7 x^{2} \times 8 x \times 12

Multiply

More Steps

Multiply the terms

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

Multiply the terms

More Steps

Evaluate

7 \times 8 \times 12

Multiply the terms

56 \times 12

Multiply the numbers

672

672 x^{2} \times x

Multiply the terms with the same base by adding their exponents

672 x^{2 + 1}

Add the numbers

672 x^{3}

x^{4} - 2 x^{3} - 672 x^{3}

Subtract the terms

More Steps

Evaluate

- 2 x^{3} - 672 x^{3}

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

(- 2 - 672) x^{3}

Subtract the numbers

- 674 x^{3}

x^{4} - 674 x^{3}

Rewrite the expression

x^{3} \times x - x^{3} \times 674

Solution

x^{3} (x - 674)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 674

Evaluate

x^{4} - 2 x^{3} - 7 x^{2} \times 8 x \times 12

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

x^{4} - 2 x^{3} - 7 x^{2} \times 8 x \times 12 = 0

Multiply

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Multiply the terms

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

Multiply the terms

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Evaluate

7 \times 8 \times 12

Multiply the terms

56 \times 12

Multiply the numbers

672

672 x^{2} \times x

Multiply the terms with the same base by adding their exponents

672 x^{2 + 1}

Add the numbers

672 x^{3}

x^{4} - 2 x^{3} - 672 x^{3} = 0

Subtract the terms

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Simplify

x^{4} - 2 x^{3} - 672 x^{3}

Subtract the terms

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Evaluate

- 2 x^{3} - 672 x^{3}

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

(- 2 - 672) x^{3}

Subtract the numbers

- 674 x^{3}

x^{4} - 674 x^{3}

x^{4} - 674 x^{3} = 0

Factor the expression

x^{3} (x - 674) = 0

Separate the equation into 2 possible cases

x^{3} = 0 x - 674 = 0

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

x = 0 x - 674 = 0

Solve the equation

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Evaluate

x - 674 = 0

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

x = 0 + 674

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

x = 674

x = 0 x = 674

Solution

x_{1} = 0, x_{2} = 674

Show Solution