Solve 3c^3-12c^4+9c^5

Question

Factor the expression

3 c^{3} (1 - c) (1 - 3 c)

Evaluate

3 c^{3} - 12 c^{4} + 9 c^{5}

Rewrite the expression

3 c^{3} - 3 c^{3} \times 4 c + 3 c^{3} \times 3 c^{2}

Factor out 3 c^{3} from the expression

3 c^{3} (1 - 4 c + 3 c^{2})

Solution

More Steps

Evaluate

1 - 4 c + 3 c^{2}

Rewrite the expression

1 + (- 3 - 1) c + 3 c^{2}

Calculate

1 - 3 c - c + 3 c^{2}

Rewrite the expression

1 - 3 c - c + c \times 3 c

Factor out - c from the expression

1 - 3 c - c (1 - 3 c)

Factor out 1 - 3 c from the expression

(1 - c) (1 - 3 c)

3 c^{3} (1 - c) (1 - 3 c)

Show Solution

c_{1} = 0, c_{2} = \frac{1}{3}, c_{3} = 1

Alternative Form

c_{1} = 0, c_{2} = 0. \dot{3}, c_{3} = 1

Evaluate

3 c^{3} - 12 c^{4} + 9 c^{5}

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

3 c^{3} - 12 c^{4} + 9 c^{5} = 0

Factor the expression

3 c^{3} (1 - c) (1 - 3 c) = 0

Divide both sides

c^{3} (1 - c) (1 - 3 c) = 0

Separate the equation into 3 possible cases

c^{3} = 0 1 - c = 0 1 - 3 c = 0

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

c = 0 1 - c = 0 1 - 3 c = 0

Solve the equation

More Steps

Evaluate

1 - c = 0

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

- c = 0 - 1

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

- c = - 1

Change the signs on both sides of the equation

c = 1

c = 0 c = 1 1 - 3 c = 0

Solve the equation

More Steps

Evaluate

1 - 3 c = 0

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

- 3 c = 0 - 1

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

- 3 c = - 1

Change the signs on both sides of the equation

3 c = 1

Divide both sides

\frac{3 c}{3} = \frac{1}{3}

Divide the numbers

c = \frac{1}{3}

c = 0 c = 1 c = \frac{1}{3}

Solution

c_{1} = 0, c_{2} = \frac{1}{3}, c_{3} = 1

Alternative Form

c_{1} = 0, c_{2} = 0. \dot{3}, c_{3} = 1

Show Solution