Solve (x-4)(x^3)(x-2)(x^5)

Question

Simplify the expression

x^{10} - 6 x^{9} + 8 x^{8}

Evaluate

(x - 4) x^{3} (x - 2) x^{5}

Multiply the terms with the same base by adding their exponents

(x - 4) x^{3 + 5} (x - 2)

Add the numbers

(x - 4) x^{8} (x - 2)

Multiply the first two terms

x^{8} (x - 4) (x - 2)

Multiply the terms

More Steps

Evaluate

x^{8} (x - 4)

Apply the distributive property

x^{8} \times x - x^{8} \times 4

Multiply the terms

More Steps

Evaluate

x^{8} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{8 + 1}

Add the numbers

x^{9}

x^{9} - x^{8} \times 4

Use the commutative property to reorder the terms

x^{9} - 4 x^{8}

(x^{9} - 4 x^{8}) (x - 2)

Apply the distributive property

x^{9} \times x - x^{9} \times 2 - 4 x^{8} \times x - (- 4 x^{8} \times 2)

Multiply the terms

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Evaluate

x^{9} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{9 + 1}

Add the numbers

x^{10}

x^{10} - x^{9} \times 2 - 4 x^{8} \times x - (- 4 x^{8} \times 2)

Use the commutative property to reorder the terms

x^{10} - 2 x^{9} - 4 x^{8} \times x - (- 4 x^{8} \times 2)

Multiply the terms

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Evaluate

x^{8} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{8 + 1}

Add the numbers

x^{9}

x^{10} - 2 x^{9} - 4 x^{9} - (- 4 x^{8} \times 2)

Multiply the numbers

x^{10} - 2 x^{9} - 4 x^{9} - (- 8 x^{8})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{10} - 2 x^{9} - 4 x^{9} + 8 x^{8}

Solution

More Steps

Evaluate

- 2 x^{9} - 4 x^{9}

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

(- 2 - 4) x^{9}

Subtract the numbers

- 6 x^{9}

x^{10} - 6 x^{9} + 8 x^{8}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 2, x_{3} = 4

Evaluate

(x - 4) (x^{3}) (x - 2) (x^{5})

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

(x - 4) (x^{3}) (x - 2) (x^{5}) = 0

Calculate

(x - 4) x^{3} (x - 2) (x^{5}) = 0

Calculate

(x - 4) x^{3} (x - 2) x^{5} = 0

Multiply the terms

More Steps

Multiply the terms

(x - 4) x^{3} (x - 2) x^{5}

Multiply the terms with the same base by adding their exponents

(x - 4) x^{3 + 5} (x - 2)

Add the numbers

(x - 4) x^{8} (x - 2)

Multiply the first two terms

x^{8} (x - 4) (x - 2)

x^{8} (x - 4) (x - 2) = 0

Separate the equation into 3 possible cases

x^{8} = 0 x - 4 = 0 x - 2 = 0

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

x = 0 x - 4 = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 0 x = 4 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 0 x = 4 x = 2

Solution

x_{1} = 0, x_{2} = 2, x_{3} = 4

Show Solution