Solve (x-1)(x-2)(x-3)(x-7)

Question

Simplify the expression

x^{4} - 13 x^{3} + 53 x^{2} - 83 x + 42

Evaluate

(x - 1) (x - 2) (x - 3) (x - 7)

Multiply the terms

More Steps

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

Multiply the terms

More Steps

(x^{3} - 6 x^{2} + 11 x - 6) (x - 7)

Apply the distributive property

x^{3} \times x - x^{3} \times 7 - 6 x^{2} \times x - (- 6 x^{2} \times 7) + 11 x \times x - 11 x \times 7 - 6 x - (- 6 \times 7)

Multiply the terms

More Steps

x^{4} - x^{3} \times 7 - 6 x^{2} \times x - (- 6 x^{2} \times 7) + 11 x \times x - 11 x \times 7 - 6 x - (- 6 \times 7)

Use the commutative property to reorder the terms

x^{4} - 7 x^{3} - 6 x^{2} \times x - (- 6 x^{2} \times 7) + 11 x \times x - 11 x \times 7 - 6 x - (- 6 \times 7)

Multiply the terms

More Steps

x^{4} - 7 x^{3} - 6 x^{3} - (- 6 x^{2} \times 7) + 11 x \times x - 11 x \times 7 - 6 x - (- 6 \times 7)

Multiply the numbers

x^{4} - 7 x^{3} - 6 x^{3} - (- 42 x^{2}) + 11 x \times x - 11 x \times 7 - 6 x - (- 6 \times 7)

Multiply the terms

x^{4} - 7 x^{3} - 6 x^{3} - (- 42 x^{2}) + 11 x^{2} - 11 x \times 7 - 6 x - (- 6 \times 7)

Multiply the numbers

x^{4} - 7 x^{3} - 6 x^{3} - (- 42 x^{2}) + 11 x^{2} - 77 x - 6 x - (- 6 \times 7)

Multiply the numbers

x^{4} - 7 x^{3} - 6 x^{3} - (- 42 x^{2}) + 11 x^{2} - 77 x - 6 x - (- 42)

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} - 6 x^{3} + 42 x^{2} + 11 x^{2} - 77 x - 6 x + 42

Subtract the terms

More Steps

x^{4} - 13 x^{3} + 42 x^{2} + 11 x^{2} - 77 x - 6 x + 42

Add the terms

More Steps

x^{4} - 13 x^{3} + 53 x^{2} - 77 x - 6 x + 42

Solution

More Steps

x^{4} - 13 x^{3} + 53 x^{2} - 83 x + 42

Show Solution

Find the roots

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

Show Solution