Solve (x-1)(x^5)(x-6)(x 8)

Question

Simplify the expression

8 x^{8} - 56 x^{7} + 48 x^{6}

Evaluate

(x - 1) x^{5} (x - 6) (x \times 8)

Remove the parentheses

(x - 1) x^{5} (x - 6) x \times 8

Multiply the terms with the same base by adding their exponents

(x - 1) x^{5 + 1} (x - 6) \times 8

Add the numbers

(x - 1) x^{6} (x - 6) \times 8

Use the commutative property to reorder the terms

(x - 1) \times 8 x^{6} (x - 6)

Multiply the first two terms

8 x^{6} (x - 1) (x - 6)

Multiply the terms

More Steps

Evaluate

8 x^{6} (x - 1)

Apply the distributive property

8 x^{6} \times x - 8 x^{6} \times 1

Multiply the terms

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Evaluate

x^{6} \times x

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

x^{6 + 1}

Add the numbers

x^{7}

8 x^{7} - 8 x^{6} \times 1

Any expression multiplied by 1 remains the same

8 x^{7} - 8 x^{6}

(8 x^{7} - 8 x^{6}) (x - 6)

Apply the distributive property

8 x^{7} \times x - 8 x^{7} \times 6 - 8 x^{6} \times x - (- 8 x^{6} \times 6)

Multiply the terms

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Evaluate

x^{7} \times x

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

x^{7 + 1}

Add the numbers

x^{8}

8 x^{8} - 8 x^{7} \times 6 - 8 x^{6} \times x - (- 8 x^{6} \times 6)

Multiply the numbers

8 x^{8} - 48 x^{7} - 8 x^{6} \times x - (- 8 x^{6} \times 6)

Multiply the terms

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Evaluate

x^{6} \times x

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

x^{6 + 1}

Add the numbers

x^{7}

8 x^{8} - 48 x^{7} - 8 x^{7} - (- 8 x^{6} \times 6)

Multiply the numbers

8 x^{8} - 48 x^{7} - 8 x^{7} - (- 48 x^{6})

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

8 x^{8} - 48 x^{7} - 8 x^{7} + 48 x^{6}

Solution

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Evaluate

- 48 x^{7} - 8 x^{7}

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

(- 48 - 8) x^{7}

Subtract the numbers

- 56 x^{7}

8 x^{8} - 56 x^{7} + 48 x^{6}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 1, x_{3} = 6

Evaluate

(x - 1) (x^{5}) (x - 6) (x \times 8)

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

(x - 1) (x^{5}) (x - 6) (x \times 8) = 0

Calculate

(x - 1) x^{5} (x - 6) (x \times 8) = 0

Use the commutative property to reorder the terms

(x - 1) x^{5} (x - 6) \times 8 x = 0

Multiply the terms

More Steps

Multiply the terms

(x - 1) x^{5} (x - 6) \times 8 x

Multiply the terms with the same base by adding their exponents

(x - 1) x^{5 + 1} (x - 6) \times 8

Add the numbers

(x - 1) x^{6} (x - 6) \times 8

Use the commutative property to reorder the terms

(x - 1) \times 8 x^{6} (x - 6)

Multiply the first two terms

8 x^{6} (x - 1) (x - 6)

8 x^{6} (x - 1) (x - 6) = 0

Elimination the left coefficient

x^{6} (x - 1) (x - 6) = 0

Separate the equation into 3 possible cases

x^{6} = 0 x - 1 = 0 x - 6 = 0

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

x = 0 x - 1 = 0 x - 6 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = 1 x - 6 = 0

Solve the equation

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 0 x = 1 x = 6

Solution

x_{1} = 0, x_{2} = 1, x_{3} = 6

Show Solution