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

Question

Simplify the expression

2 x^{9} - 11 x^{8} + 15 x^{7}

Evaluate

x^{2} \times x^{5} (x - 3) (2 x - 5)

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{7} (x - 3) (2 x - 5)

Multiply the terms

More Steps

Evaluate

x^{7} (x - 3)

Apply the distributive property

x^{7} \times x - x^{7} \times 3

Multiply the terms

More Steps

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}

x^{8} - x^{7} \times 3

Use the commutative property to reorder the terms

x^{8} - 3 x^{7}

(x^{8} - 3 x^{7}) (2 x - 5)

Apply the distributive property

x^{8} \times 2 x - x^{8} \times 5 - 3 x^{7} \times 2 x - (- 3 x^{7} \times 5)

Multiply the terms

More Steps

Evaluate

x^{8} \times 2 x

Use the commutative property to reorder the terms

2 x^{8} \times x

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}

2 x^{9}

2 x^{9} - x^{8} \times 5 - 3 x^{7} \times 2 x - (- 3 x^{7} \times 5)

Use the commutative property to reorder the terms

2 x^{9} - 5 x^{8} - 3 x^{7} \times 2 x - (- 3 x^{7} \times 5)

Multiply the terms

More Steps

Evaluate

- 3 x^{7} \times 2 x

Multiply the numbers

- 6 x^{7} \times x

Multiply the terms

More Steps

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}

- 6 x^{8}

2 x^{9} - 5 x^{8} - 6 x^{8} - (- 3 x^{7} \times 5)

Multiply the numbers

2 x^{9} - 5 x^{8} - 6 x^{8} - (- 15 x^{7})

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

2 x^{9} - 5 x^{8} - 6 x^{8} + 15 x^{7}

Solution

More Steps

Evaluate

- 5 x^{8} - 6 x^{8}

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

(- 5 - 6) x^{8}

Subtract the numbers

- 11 x^{8}

2 x^{9} - 11 x^{8} + 15 x^{7}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5}{2}, x_{3} = 3

Alternative Form

x_{1} = 0, x_{2} = 2.5, x_{3} = 3

Evaluate

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

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

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

Calculate

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

Multiply

More Steps

Multiply the terms

x^{2} \times x^{5} (x - 3) (2 x - 5)

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{7} (x - 3) (2 x - 5)

x^{7} (x - 3) (2 x - 5) = 0

Separate the equation into 3 possible cases

x^{7} = 0 x - 3 = 0 2 x - 5 = 0

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

x = 0 x - 3 = 0 2 x - 5 = 0

Solve the equation

More Steps

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 = 3 2 x - 5 = 0

Solve the equation

More Steps

Evaluate

2 x - 5 = 0

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

2 x = 0 + 5

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

2 x = 5

Divide both sides

\frac{2 x}{2} = \frac{5}{2}

Divide the numbers

x = \frac{5}{2}

x = 0 x = 3 x = \frac{5}{2}

Solution

x_{1} = 0, x_{2} = \frac{5}{2}, x_{3} = 3

Alternative Form

x_{1} = 0, x_{2} = 2.5, x_{3} = 3

Show Solution