Solve 2x^53x-6 - ScanMath

Question

Simplify the expression

6 x^{6} - 6

Evaluate

2 x^{5} \times 3 x - 6

Solution

More Steps

Evaluate

2 x^{5} \times 3 x

Multiply the terms

6 x^{5} \times x

Multiply the terms with the same base by adding their exponents

6 x^{5 + 1}

Add the numbers

6 x^{6}

6 x^{6} - 6

Show Solution

Factor the expression

6 (x - 1) (x^{2} + x + 1) (x + 1) (x^{2} - x + 1)

Evaluate

2 x^{5} \times 3 x - 6

Evaluate

More Steps

Evaluate

2 x^{5} \times 3 x

Multiply the terms

6 x^{5} \times x

Multiply the terms with the same base by adding their exponents

6 x^{5 + 1}

Add the numbers

6 x^{6}

6 x^{6} - 6

Factor out 6 from the expression

6 (x^{6} - 1)

Factor the expression

More Steps

Evaluate

x^{6} - 1

Rewrite the expression in exponential form

(x^{3})^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(x^{3} - 1) (x^{3} + 1)

6 (x^{3} - 1) (x^{3} + 1)

Evaluate

More Steps

Evaluate

x^{3} - 1

Rewrite the expression in exponential form

x^{3} - 1^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(x - 1) (x^{2} + x \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(x - 1) (x^{2} + x + 1^{2})

1 raised to any power equals to 1

(x - 1) (x^{2} + x + 1)

6 (x - 1) (x^{2} + x + 1) (x^{3} + 1)

Solution

More Steps

Evaluate

x^{3} + 1

Rewrite the expression in exponential form

x^{3} + 1^{3}

Use a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2}) to factor the expression

(x + 1) (x^{2} - x \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(x + 1) (x^{2} - x + 1^{2})

1 raised to any power equals to 1

(x + 1) (x^{2} - x + 1)

6 (x - 1) (x^{2} + x + 1) (x + 1) (x^{2} - x + 1)

Show Solution

Find the roots

x_{1} = - 1, x_{2} = 1

Evaluate

2 x^{5} \times 3 x - 6

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

2 x^{5} \times 3 x - 6 = 0

Multiply

More Steps

Multiply the terms

2 x^{5} \times 3 x

Multiply the terms

6 x^{5} \times x

Multiply the terms with the same base by adding their exponents

6 x^{5 + 1}

Add the numbers

6 x^{6}

6 x^{6} - 6 = 0

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

6 x^{6} = 0 + 6

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

6 x^{6} = 6

Divide both sides

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

Divide the numbers

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

Divide the numbers

More Steps

Evaluate

\frac{6}{6}

Reduce the numbers

\frac{1}{1}

Calculate

1

x^{6} = 1

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

x = \pm 61

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

Solution

x_{1} = - 1, x_{2} = 1

Show Solution