Solve (x^5)(x^3)(x-4)(x-6)(x-7)

Question

Simplify the expression

x^{11} - 17 x^{10} + 94 x^{9} - 168 x^{8}

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{8} (x - 4) (x - 6) (x - 7)

Multiply the terms

More Steps

(x^{9} - 4 x^{8}) (x - 6) (x - 7)

Multiply the terms

More Steps

(x^{10} - 10 x^{9} + 24 x^{8}) (x - 7)

Apply the distributive property

x^{10} \times x - x^{10} \times 7 - 10 x^{9} \times x - (- 10 x^{9} \times 7) + 24 x^{8} \times x - 24 x^{8} \times 7

Multiply the terms

More Steps

x^{11} - x^{10} \times 7 - 10 x^{9} \times x - (- 10 x^{9} \times 7) + 24 x^{8} \times x - 24 x^{8} \times 7

Use the commutative property to reorder the terms

x^{11} - 7 x^{10} - 10 x^{9} \times x - (- 10 x^{9} \times 7) + 24 x^{8} \times x - 24 x^{8} \times 7

Multiply the terms

More Steps

x^{11} - 7 x^{10} - 10 x^{10} - (- 10 x^{9} \times 7) + 24 x^{8} \times x - 24 x^{8} \times 7

Multiply the numbers

x^{11} - 7 x^{10} - 10 x^{10} - (- 70 x^{9}) + 24 x^{8} \times x - 24 x^{8} \times 7

Multiply the terms

More Steps

x^{11} - 7 x^{10} - 10 x^{10} - (- 70 x^{9}) + 24 x^{9} - 24 x^{8} \times 7

Multiply the numbers

x^{11} - 7 x^{10} - 10 x^{10} - (- 70 x^{9}) + 24 x^{9} - 168 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^{11} - 7 x^{10} - 10 x^{10} + 70 x^{9} + 24 x^{9} - 168 x^{8}

Subtract the terms

More Steps

x^{11} - 17 x^{10} + 70 x^{9} + 24 x^{9} - 168 x^{8}

Solution

More Steps

x^{11} - 17 x^{10} + 94 x^{9} - 168 x^{8}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 4, x_{3} = 6, x_{4} = 7

Show Solution