Solve 8-4a-2a^3+a^4

Question

Factor the expression

(2 - a) (4 - a^{3})

Evaluate

8 - 4 a - 2 a^{3} + a^{4}

Calculate

8 - 2 a^{3} - 4 a + a^{4}

Rewrite the expression

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

Factor out 2 from the expression

2 (4 - a^{3}) - a \times 4 + a \times a^{3}

Factor out - a from the expression

2 (4 - a^{3}) - a (4 - a^{3})

Solution

(2 - a) (4 - a^{3})

Show Solution

a_{1} = 34, a_{2} = 2

Alternative Form

a_{1} \approx 1.587401, a_{2} = 2

Evaluate

8 - 4 a - 2 a^{3} + a^{4}

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

8 - 4 a - 2 a^{3} + a^{4} = 0

Factor the expression

(2 - a) (4 - a^{3}) = 0

Separate the equation into 2 possible cases

2 - a = 0 4 - a^{3} = 0

Solve the equation

More Steps

Evaluate

2 - a = 0

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

- a = 0 - 2

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

- a = - 2

Change the signs on both sides of the equation

a = 2

a = 2 4 - a^{3} = 0

Solve the equation

More Steps

Evaluate

4 - a^{3} = 0

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

- a^{3} = 0 - 4

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

- a^{3} = - 4

Change the signs on both sides of the equation

a^{3} = 4

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

3 a^{3} = 34

Calculate

a = 34

a = 2 a = 34

Solution

a_{1} = 34, a_{2} = 2

Alternative Form

a_{1} \approx 1.587401, a_{2} = 2

Show Solution