Factor the polynomial completely.

x2 - x - 40


Group of answer choices

(x - 40)(x + 1)

(x + 5)(x - 8)

(x - 5)(x + 8)

prime polynomial

We are asked to factor the quadratic polynomial \( x^2 - x - 40 \). Let's go through the steps:

1. Identify the quadratic form:  
   The given expression is of the form \( ax^2 + bx + c \), where:
   - \( a = 1 \) (coefficient of \( x^2 \)),
   - \( b = -1 \) (coefficient of \( x \)),
   - \( c = -40 \) (constant term).

2. Find two numbers that multiply to give \( ac = 1 \times -40 = -40 \) and add to give \( b = -1 \).  
   These two numbers are \( -8 \) and \( 5 \), because:
   - \( -8 \times 5 = -40 \),
   - \( -8 + 5 = -1 \).

3. Use these numbers to factor the quadratic:  
   So, the factorization of \( x^2 - x - 40 \) is:
   \[
   (x - 8)(x + 5)
   \]

Thus, the correct factorization is \( (x - 8)(x + 5) \).

### The correct answer is:
**\( (x + 5)(x - 8) \)**

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Factor the polynomial \( x^2 - 6x + 8 \).
2. Factor \( x^2 - 16 \).
3. Factor \( x^2 + 7x + 12 \).
4. What is the factored form of \( x^2 - 9x + 20 \)?
5. Is \( x^2 + 4x + 5 \) factorable over the real numbers?

**Tip:** Always check if the quadratic can be factored by finding two numbers that multiply to the constant term and add to the coefficient of the linear term.

Factor the polynomial completely. x^2 - x - 40

Learn how to factor the quadratic polynomial x^2 - x - 40 with a detailed step-by-step solution. This problem involves factoring quadratics by finding two numbers that multiply to -40 and add to -1. Ideal for students in Grades 8-10 studying algebra and quadratic equations.

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