Solve 2z^5- 12z^310z

Question

Simplify the expression

2 z^{5} - 120 z^{4}

Evaluate

2 z^{5} - 12 z^{3} \times 10 z

Solution

More Steps

Evaluate

12 z^{3} \times 10 z

Multiply the terms

120 z^{3} \times z

Multiply the terms with the same base by adding their exponents

120 z^{3 + 1}

Add the numbers

120 z^{4}

2 z^{5} - 120 z^{4}

Show Solution

2 z^{4} (z - 60)

Evaluate

2 z^{5} - 12 z^{3} \times 10 z

Multiply

More Steps

Evaluate

12 z^{3} \times 10 z

Multiply the terms

120 z^{3} \times z

Multiply the terms with the same base by adding their exponents

120 z^{3 + 1}

Add the numbers

120 z^{4}

2 z^{5} - 120 z^{4}

Rewrite the expression

2 z^{4} \times z - 2 z^{4} \times 60

Solution

2 z^{4} (z - 60)

Show Solution

z_{1} = 0, z_{2} = 60

Evaluate

2 z^{5} - 12 z^{3} \times 10 z

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

2 z^{5} - 12 z^{3} \times 10 z = 0

Multiply

More Steps

Multiply the terms

12 z^{3} \times 10 z

Multiply the terms

120 z^{3} \times z

Multiply the terms with the same base by adding their exponents

120 z^{3 + 1}

Add the numbers

120 z^{4}

2 z^{5} - 120 z^{4} = 0

Factor the expression

2 z^{4} (z - 60) = 0

Divide both sides

z^{4} (z - 60) = 0

Separate the equation into 2 possible cases

z^{4} = 0 z - 60 = 0

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

z = 0 z - 60 = 0

Solve the equation

More Steps

Evaluate

z - 60 = 0

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

z = 0 + 60

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

z = 60

z = 0 z = 60

Solution

z_{1} = 0, z_{2} = 60

Show Solution