Solve (x^2)(x-1)(x-3)(4x^(3))

Question

Simplify the expression

4 x^{7} - 16 x^{6} + 12 x^{5}

Evaluate

x^{2} (x - 1) (x - 3) \times 4 x^{3}

Multiply the terms with the same base by adding their exponents

x^{2 + 3} (x - 1) (x - 3) \times 4

Add the numbers

x^{5} (x - 1) (x - 3) \times 4

Use the commutative property to reorder the terms

4 x^{5} (x - 1) (x - 3)

Multiply the terms

More Steps

Evaluate

4 x^{5} (x - 1)

Apply the distributive property

4 x^{5} \times x - 4 x^{5} \times 1

Multiply the terms

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Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

4 x^{6} - 4 x^{5} \times 1

Any expression multiplied by 1 remains the same

4 x^{6} - 4 x^{5}

(4 x^{6} - 4 x^{5}) (x - 3)

Apply the distributive property

4 x^{6} \times x - 4 x^{6} \times 3 - 4 x^{5} \times x - (- 4 x^{5} \times 3)

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}

4 x^{7} - 4 x^{6} \times 3 - 4 x^{5} \times x - (- 4 x^{5} \times 3)

Multiply the numbers

4 x^{7} - 12 x^{6} - 4 x^{5} \times x - (- 4 x^{5} \times 3)

Multiply the terms

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Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

4 x^{7} - 12 x^{6} - 4 x^{6} - (- 4 x^{5} \times 3)

Multiply the numbers

4 x^{7} - 12 x^{6} - 4 x^{6} - (- 12 x^{5})

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

4 x^{7} - 12 x^{6} - 4 x^{6} + 12 x^{5}

Solution

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Evaluate

- 12 x^{6} - 4 x^{6}

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

(- 12 - 4) x^{6}

Subtract the numbers

- 16 x^{6}

4 x^{7} - 16 x^{6} + 12 x^{5}

Show Solution

Find the roots

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

Evaluate

(x^{2}) (x - 1) (x - 3) (4 x^{3})

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

(x^{2}) (x - 1) (x - 3) (4 x^{3}) = 0

Calculate

x^{2} (x - 1) (x - 3) (4 x^{3}) = 0

Multiply the terms

x^{2} (x - 1) (x - 3) \times 4 x^{3} = 0

Multiply

More Steps

Multiply the terms

x^{2} (x - 1) (x - 3) \times 4 x^{3}

Multiply the terms with the same base by adding their exponents

x^{2 + 3} (x - 1) (x - 3) \times 4

Add the numbers

x^{5} (x - 1) (x - 3) \times 4

Use the commutative property to reorder the terms

4 x^{5} (x - 1) (x - 3)

4 x^{5} (x - 1) (x - 3) = 0

Elimination the left coefficient

x^{5} (x - 1) (x - 3) = 0

Separate the equation into 3 possible cases

x^{5} = 0 x - 1 = 0 x - 3 = 0

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

x = 0 x - 1 = 0 x - 3 = 0

Solve the equation

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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 - 3 = 0

Solve the equation

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Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 0 x = 1 x = 3

Solution

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

Show Solution