Solve 8f -5f -9f^4f

Question

Simplify the expression

3 f - 9 f^{5}

Evaluate

8 f - 5 f - 9 f^{4} \times f

Multiply

More Steps

Multiply the terms

- 9 f^{4} \times f

Multiply the terms with the same base by adding their exponents

- 9 f^{4 + 1}

Add the numbers

- 9 f^{5}

8 f - 5 f - 9 f^{5}

Solution

More Steps

Evaluate

8 f - 5 f

Collect like terms by calculating the sum or difference of their coefficients

(8 - 5) f

Subtract the numbers

3 f

3 f - 9 f^{5}

Show Solution

Factor the expression

3 f (1 - 3 f^{4})

Evaluate

8 f - 5 f - 9 f^{4} \times f

Multiply

More Steps

Multiply the terms

9 f^{4} \times f

Multiply the terms with the same base by adding their exponents

9 f^{4 + 1}

Add the numbers

9 f^{5}

8 f - 5 f - 9 f^{5}

Subtract the terms

More Steps

Simplify

8 f - 5 f

Collect like terms by calculating the sum or difference of their coefficients

(8 - 5) f

Subtract the numbers

3 f

3 f - 9 f^{5}

Rewrite the expression

3 f - 3 f \times 3 f^{4}

Solution

3 f (1 - 3 f^{4})

Show Solution

Find the roots

f_{1} = - \frac{4 27}{3}, f_{2} = 0, f_{3} = \frac{4 27}{3}

Alternative Form

f_{1} \approx - 0.759836, f_{2} = 0, f_{3} \approx 0.759836

Evaluate

8 f - 5 f - 9 f^{4} \times f

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

8 f - 5 f - 9 f^{4} \times f = 0

Multiply

More Steps

Multiply the terms

9 f^{4} \times f

Multiply the terms with the same base by adding their exponents

9 f^{4 + 1}

Add the numbers

9 f^{5}

8 f - 5 f - 9 f^{5} = 0

Subtract the terms

More Steps

Simplify

8 f - 5 f

Collect like terms by calculating the sum or difference of their coefficients

(8 - 5) f

Subtract the numbers

3 f

3 f - 9 f^{5} = 0

Factor the expression

3 f (1 - 3 f^{4}) = 0

Divide both sides

f (1 - 3 f^{4}) = 0

Separate the equation into 2 possible cases

f = 0 1 - 3 f^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 3 f^{4} = 0

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

- 3 f^{4} = 0 - 1

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

- 3 f^{4} = - 1

Change the signs on both sides of the equation

3 f^{4} = 1

Divide both sides

\frac{3 f ^{4}}{3} = \frac{1}{3}

Divide the numbers

f^{4} = \frac{1}{3}

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

f = \pm 4 \frac{1}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{3}

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

\frac{4 1}{4 3}

Simplify the radical expression

\frac{1}{4 3}

Multiply by the Conjugate

\frac{4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 27}{3}

f = \pm \frac{4 27}{3}

Separate the equation into 2 possible cases

f = \frac{4 27}{3} f = - \frac{4 27}{3}

f = 0 f = \frac{4 27}{3} f = - \frac{4 27}{3}

Solution

f_{1} = - \frac{4 27}{3}, f_{2} = 0, f_{3} = \frac{4 27}{3}

Alternative Form

f_{1} \approx - 0.759836, f_{2} = 0, f_{3} \approx 0.759836

Show Solution