Solve x^{4} 3x^{3} 10x^{2}-5x^6

Question

Simplify the expression

Solution

30 x^{9} - 5 x^{6}

Evaluate

x^{4} \times 3 x^{3} \times 10 x^{2} - 5 x^{6}

Solution

More Steps

Evaluate

x^{4} \times 3 x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 3 + 2} \times 3 \times 10

Add the numbers

x^{9} \times 3 \times 10

Multiply the terms

x^{9} \times 30

Use the commutative property to reorder the terms

30 x^{9}

30 x^{9} - 5 x^{6}

Show Solution

Factor the expression

Factor

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

Evaluate

x^{4} \times 3 x^{3} \times 10 x^{2} - 5 x^{6}

Multiply

More Steps

Evaluate

x^{4} \times 3 x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 3 + 2} \times 3 \times 10

Add the numbers

x^{9} \times 3 \times 10

Multiply the terms

x^{9} \times 30

Use the commutative property to reorder the terms

30 x^{9}

30 x^{9} - 5 x^{6}

Rewrite the expression

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

Solution

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

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = 0, x_{2} = \frac{3 36}{6}

Alternative Form

x_{1} = 0, x_{2} \approx 0.550321

Evaluate

x^{4} \times 3 x^{3} \times 10 x^{2} - 5 x^{6}

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

x^{4} \times 3 x^{3} \times 10 x^{2} - 5 x^{6} = 0

Multiply

More Steps

Multiply the terms

x^{4} \times 3 x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 3 + 2} \times 3 \times 10

Add the numbers

x^{9} \times 3 \times 10

Multiply the terms

x^{9} \times 30

Use the commutative property to reorder the terms

30 x^{9}

30 x^{9} - 5 x^{6} = 0

Factor the expression

5 x^{6} (6 x^{3} - 1) = 0

Divide both sides

x^{6} (6 x^{3} - 1) = 0

Separate the equation into 2 possible cases

x^{6} = 0 6 x^{3} - 1 = 0

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

x = 0 6 x^{3} - 1 = 0

Solve the equation

More Steps

Evaluate

6 x^{3} - 1 = 0

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

6 x^{3} = 0 + 1

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

6 x^{3} = 1

Divide both sides

\frac{6 x ^{3}}{6} = \frac{1}{6}

Divide the numbers

x^{3} = \frac{1}{6}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{6}

Calculate

x = 3 \frac{1}{6}

Simplify the root

More Steps

Evaluate

3 \frac{1}{6}

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

\frac{3 1}{3 6}

Simplify the radical expression

\frac{1}{3 6}

Multiply by the Conjugate

\frac{3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 36}{6}

x = \frac{3 36}{6}

x = 0 x = \frac{3 36}{6}

Solution

x_{1} = 0, x_{2} = \frac{3 36}{6}

Alternative Form

x_{1} = 0, x_{2} \approx 0.550321

Show Solution

X^{4} 3x^{3} 10x^{2} 5x^6

Simplify the expression

Factor the expression

Find the roots