Solve x(x-2)(x-3)(x-7)

Question

Simplify the expression

x^{4} - 12 x^{3} + 41 x^{2} - 42 x

Evaluate

x (x - 2) (x - 3) (x - 7)

Multiply the terms

More Steps

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

Multiply the terms

More Steps

(x^{3} - 5 x^{2} + 6 x) (x - 7)

Apply the distributive property

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

Multiply the terms

More Steps

x^{4} - x^{3} \times 7 - 5 x^{2} \times x - (- 5 x^{2} \times 7) + 6 x \times x - 6 x \times 7

Use the commutative property to reorder the terms

x^{4} - 7 x^{3} - 5 x^{2} \times x - (- 5 x^{2} \times 7) + 6 x \times x - 6 x \times 7

Multiply the terms

More Steps

x^{4} - 7 x^{3} - 5 x^{3} - (- 5 x^{2} \times 7) + 6 x \times x - 6 x \times 7

Multiply the numbers

x^{4} - 7 x^{3} - 5 x^{3} - (- 35 x^{2}) + 6 x \times x - 6 x \times 7

Multiply the terms

x^{4} - 7 x^{3} - 5 x^{3} - (- 35 x^{2}) + 6 x^{2} - 6 x \times 7

Multiply the numbers

x^{4} - 7 x^{3} - 5 x^{3} - (- 35 x^{2}) + 6 x^{2} - 42 x

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^{4} - 7 x^{3} - 5 x^{3} + 35 x^{2} + 6 x^{2} - 42 x

Subtract the terms

More Steps

x^{4} - 12 x^{3} + 35 x^{2} + 6 x^{2} - 42 x

Solution

More Steps

x^{4} - 12 x^{3} + 41 x^{2} - 42 x

Show Solution

Find the roots

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

Show Solution