Solve 2x^5-3x^4 6x^3

Question

Simplify the expression

2 x^{5} - 18 x^{7}

Evaluate

2 x^{5} - 3 x^{4} \times 6 x^{3}

Solution

More Steps

Evaluate

3 x^{4} \times 6 x^{3}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

18 x^{4 + 3}

Add the numbers

18 x^{7}

2 x^{5} - 18 x^{7}

Show Solution

Factor the expression

2 x^{5} (1 - 3 x) (1 + 3 x)

Evaluate

2 x^{5} - 3 x^{4} \times 6 x^{3}

Evaluate

More Steps

Evaluate

3 x^{4} \times 6 x^{3}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

18 x^{4 + 3}

Add the numbers

18 x^{7}

2 x^{5} - 18 x^{7}

Factor out 2 x^{5} from the expression

2 x^{5} (1 - 9 x^{2})

Solution

More Steps

Evaluate

1 - 9 x^{2}

Rewrite the expression in exponential form

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

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

(1 - 3 x) (1 + 3 x)

2 x^{5} (1 - 3 x) (1 + 3 x)

Show Solution

Find the roots

x_{1} = - \frac{1}{3}, x_{2} = 0, x_{3} = \frac{1}{3}

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0, x_{3} = 0. \dot{3}

Evaluate

2 x^{5} - 3 x^{4} \times 6 x^{3}

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

2 x^{5} - 3 x^{4} \times 6 x^{3} = 0

Multiply

More Steps

Multiply the terms

3 x^{4} \times 6 x^{3}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

18 x^{4 + 3}

Add the numbers

18 x^{7}

2 x^{5} - 18 x^{7} = 0

Factor the expression

2 x^{5} (1 - 9 x^{2}) = 0

Divide both sides

x^{5} (1 - 9 x^{2}) = 0

Separate the equation into 2 possible cases

x^{5} = 0 1 - 9 x^{2} = 0

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

x = 0 1 - 9 x^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 9 x^{2} = 0

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

- 9 x^{2} = 0 - 1

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

- 9 x^{2} = - 1

Change the signs on both sides of the equation

9 x^{2} = 1

Divide both sides

\frac{9 x ^{2}}{9} = \frac{1}{9}

Divide the numbers

x^{2} = \frac{1}{9}

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

x = \pm \frac{1}{9}

Simplify the expression

More Steps

Evaluate

\frac{1}{9}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{9}

Simplify the radical expression

\frac{1}{9}

Simplify the radical expression

\frac{1}{3}

x = \pm \frac{1}{3}

Separate the equation into 2 possible cases

x = \frac{1}{3} x = - \frac{1}{3}

x = 0 x = \frac{1}{3} x = - \frac{1}{3}

Solution

x_{1} = - \frac{1}{3}, x_{2} = 0, x_{3} = \frac{1}{3}

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0, x_{3} = 0. \dot{3}

Show Solution