Which is an equation with a degree of 4 and x-intercepts located at (−1,0), (−5,0), (3,0) and (4,0)?
Select the correct answer below:


y=(x+1)(x+5)(x+3)(x+4)

y=(x+1)(x+5)(x−3)(x−4)

y=(x−1)(x−5)(x+3)(x+4)

y=(x−1)(x−5)(x−3)(x−4)

y=(x+1)(x−5)(x+3)(x+4)

The degree of the equation is 4, meaning it should be a product of four linear factors, each corresponding to an x-intercept. The x-intercepts are given as \((-1,0)\), \((-5,0)\), \((3,0)\), and \((4,0)\). These intercepts correspond to the roots of the equation.

The factors of the equation are formed by the expression \((x - \text{root})\) for each x-intercept.

- For \((-1, 0)\), the factor is \((x + 1)\).
- For \((-5, 0)\), the factor is \((x + 5)\).
- For \((3, 0)\), the factor is \((x - 3)\).
- For \((4, 0)\), the factor is \((x - 4)\).

Therefore, the correct equation is:

\[
y = (x + 1)(x + 5)(x - 3)(x - 4)
\]

The correct answer is:

**y = (x + 1)(x + 5)(x - 3)(x - 4)**

Would you like more details on how the factors relate to the intercepts, or do you have any other questions?

Here are 5 related questions to consider:
1. What happens if one of the intercepts is a repeated root?
2. How do you find the degree of a polynomial given its equation?
3. How do the signs of the factors affect the location of the x-intercepts?
4. What does the shape of a fourth-degree polynomial typically look like?
5. How would you find the y-intercept of this polynomial?

**Tip**: The degree of a polynomial tells you how many roots (or x-intercepts) it can have, considering multiplicity!

Which is an equation with a degree of 4 and x-intercepts located at (−1,0), (−5,0), (3,0), and (4,0)?

Explore how to form a fourth-degree polynomial equation with roots at (-1, -5, 3, 4). This problem involves key algebraic concepts like polynomial factorization and the relationship between roots and x-intercepts. Ideal for students in Grades 9-12.

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